Patent Grant
8837793
The present invention relates to radioactive-emission measurements of a volume. More particularly, the present invention relates to the accurate reconstruction of the volume, based on measurements from non-uniform views of a volume, and on the dynamic selection of views during the data acquisition process. Of particular interest is view selection for medical imaging and/or in conjunction with medical instruments, such as guided minimally invasive surgical instruments.
Radionuclide imaging is one of the most important applications of radioactivity in medicine. Its purpose is to obtain a distribution image of a radioactively labeled substance, e.g., a radiopharmaceutical, within the body following administration thereof to a patient. Radioactive-emission imaging relies on the fact that in general, pathologies, such as malignant tumors, malfunctioning organs, and inflammations, display a level of activity different from that of healthy tissue. Thus, radiopharmaceuticals, which circulate in the blood stream, are picked up by the active pathologies to a different extent than by the surrounding healthy tissue; in consequence, the pathologies are operative as radioactive-emission sources and may be detected by radioactive-emission imaging. It will be appreciated that the pathology may appear as a concentrated source of high radiation, a hot region, as may be associated with a tumor, or as a region of low-level radiation, which is nonetheless above the background level, as may be associated with carcinoma.
A reversed situation is similarly possible. Dead tissue has practically no pick up of radiopharmaceuticals, and is thus operative as a cold region.
Thus radiopharmaceuticals may be used for identifying active pathologies as well as dead tissue.
In the discussion that follows, the term body structure is intended to include organs, portions of organs, a part of the body, and a whole body. The term organ target is intended to include pathological features within organs. These pathological features may be expressed, by radioactive-emission imaging, as any one of the following:
i. hot regions, of a radioactive emission intensity higher than the background level;
ii. regions of low-level radioactive emission intensity, which is nonetheless above the background level; and
iii cold regions, of a radioactive emission intensity, lower than the background level.
Examples of radiopharmaceuticals include monoclonal antibodies or other agents, e.g., fibrinogen or fluorodeoxyglucose, tagged with a radioactive isotope, e.g., 99Mtechnetium, 67gallium, 201thallium, 111indium, 123iodine, 125iodine and 18fluorine, which may be administered orally or intravenously. The radiopharmaceuticals are designed to concentrate in the area of a tumor, and the uptake of such radiopharmaceuticals in the active part of a tumor, or other pathologies such as an inflammation, is higher and more rapid than in the tissue that neighbors the tumor. Thereafter, a radiation-emission-measuring-probe, which may be configured for extracorporeal or intracorporeal use, is employed for locating the position of the active area. Another application is the detection of blood clots with radiopharmaceuticals such as ACUTECT from Nycomed Amersham for the detection of newly formed thrombosis in veins, or clots in arteries of the heart or brain, in an emergency or operating room. Yet other applications include radioimaging of myocardial infarct using agents such as radioactive anti-myosin antibodies, radioimaging specific cell types using radioactively tagged molecules (also known as molecular imaging), etc.
The usual preferred emission for such applications is that of gamma rays, which emission is in the energy range of approximately 11-511 KeV. Beta radiation and positrons may also be detected.
Radioactive-emission imaging is performed with a radioactive-emission-measuring detector, such as a room temperature, solid-state CdZnTe (CZT) detector, which is among the more promising that are currently available. It may be configured as a single-pixel or a multi-pixel detector. Alternatively, another solid-state detector such as CdTe, HgI, Si, Ge, or the like, or a combination of a scintillation detector (such as NaT(Tl), LSO, GSO, CsI, CaF, or the like) and a photomultiplier, or another detector as known, may be used.
1
a-1i schematically illustrate detecting units 102 and detecting blocks 101 of various geometries and constructions, and radioactive-emission-measuring probes associated with them.
a schematically illustrates a detecting unit 102, formed as a single-pixel detector 104, for example, a room-temperature solid-state CdZnTe (CZT) detector, having a diameter D and a thickness τd. Both the detector diameter D, or a diameter equivalent in the case of a non-circular detector, and the detector thickness τd affect the detecting efficiency. The detector diameter determines the surface area on which radioactive emission impinges; the greater the surface area, the greater the efficiency. The detector thickness affects the stopping power of the detector. High energy gamma rays may go through a thin detector, and the probability of their detection increases with detector thickness. By itself, a single-pixel detector cannot generate an image; rather, all counts are distributed over the surface area of the detector.
b schematically illustrates the detecting unit 102 with a collimator 108, formed as a single cell of a diameter D, a length L, and a septa thickness τ, attached to the detector 104. The collimator 108 may be, for example, of lead, tungsten or another material which substantially blocks gamma and beta rays.
The collimator's geometry, and specifically, the ratio of D/L, provides the detecting unit 102 with a collection angle δ analogous to a viewing angle of an optical camera. The collection angle δ limits the radioactive-emission detection to substantially only that radioactive emission, which impinges on the detector 104 after passing through a “corridor” of the collimator 108 (although in practice, some high-energy gamma rays may penetrate the collimator's walls).
c schematically illustrates a block 101 of the detecting units 102, with the collimator 108, formed as a multi-cell collimator, of a cell diameter D. The collection angle δ is defined for each of the detecting units 102 in the block, and each of the detecting units 102 forms a pixel in the block 101.
d schematically illustrates a radioactive-emission-measuring probe 100 which comprises several detecting units 102, of different geometries and different collection angles δ, within a housing 107.
e-1i schematically illustrate the block 101, formed as a combination of a scintillation detector (such as NaI(Tl), LSO, GSO, CsI, CaF, or the like), a collimator grid, and photomultipliers.
As seen in
The distal view 111 of the collimator grid is seen in
Two optional proximal views 109 of the photomultipliers 103 are seen in
An Anger camera 117, of the block 101 in the housing 107 is seen in
In each of the cases of
i. The detection efficiency is the ratio of measured radiation to emitted radiation; and
ii. The image resolution is the capability of making distinguishable closely adjacent radioactive-emission organ targets, or the capability to accurately determine the size and shape of individual radioactive-emission organ targets.
Naturally, it is desired to optimize both the detection efficiency and the image resolution. Yet, they are inversely related to each other. The detection efficiency increases with increasing collimator's collection angle, and the image resolution decreases with increasing collimator's collection angle. For example, when the ratio of D/L is 1/2, the collection angle δ is substantially 2.5 steradians, so the cell views incident radiation within the confinement of about a 2.5-steradian sector. However, when the ratio of D/L is 1/12, the collection angle δ is substantially 0.31 steradians, so the cell views incident radiation within the confinement of about a 0.31-steradian sector.
Once the emission data is obtained, the data is processed to reconstruct the intensity distribution within the measured volume. The reconstruction process is generally complex, due to the large quantity of data which must be processed in order to obtain an accurate reconstruction. The following statistical model may be used to perform reconstruction.
We assume an intensity distribution, I, defined over an input space U, where U comprises a set of basic elements (e.g., pixels in two dimensional spaces, voxels in three dimensional spaces), and I(u) is the intensity of a given basic element uεU. A detecting unit positioned on a radiation-emission-measuring-probe takes a series of measurements y=(yi)i=1T from different positions and orientations around the volume U. The geometrical and physical properties of the detecting unit, together with its position and orientation in a given measurement i, determine the detection probability φi(u) of a photon emitted from location u. Thus the effective intensity of location u as viewed by the detecting unit during measurement i is φi(u)I(u).
The random count Xi(u) of photons that are emitted from location u and detected in measurement i is modeled by a Poisson process with mean φi(i)I(u). The total count of photons detected in measurement i is thus:
yi˜Poisson(ΣuεUφi(u)I(u)) (1a)
or in matrix notation:
y=Poisson(ΦI) (1b)
where y is the vector of measurements yi, Φ is a matrix of detection probabilities over measurements i and voxels u, and I is a vector of intensity per voxel u. The reconstruction problem is to reconstruct the intensities I from the measurements y.
The 2-D Radon transform is a mathematical relationship which may be used to reconstruct the emission intensities of volume U when the set of measurements (yt)t=1T is unconstrained. The Radon transform is not statistical and does not take into account the Poissonian nature of the counts. In addition, it models the views as line projections. The Radon transform maps the spatial domain (x,y) to the Radon domain (p,φ). For a fixed projection angle, the Radon transform is simply a projection of the object. A technique known in the art as filtered back-projection (FBP) uses a back-projection operator and the inverse of the Radon transform to reconstruct the intensity distribution in volume U from measurements (yt)t=1T.
The basic, idealized problem solved by the FBP approach is to reconstruct an image from its Radon transform. The Radon transform, when properly defined, has a well-defined inverse. However, in order to invert the transform one needs measured data spanning 180°. In many medical imaging situations, the positioning of the detecting unit relative to the emitting object is constrained, so that complete measured data is not available. Reconstruction based on filtered back-projection is therefore of limited use for medical imaging. Maximum likelihood (ML) and Maximum A Posteriori (MAP) estimation methods, which address the statistical nature of the counts, have been found to provide better image reconstructions than FBP.
Limited-angle tomography is a reconstruction technique in the related art which reconstructs an image from projections acquired over a limited range of angular directions. The success of the reconstruction process depends upon the extent of the angular range acquired compared with the angular range of the missing projections. Any reconstruction from a limited range of projections potentially results in spatial distortions (artifacts) in the image. Limited angle techniques can be applied for both the Radon transform and the statistical models, but better results are generally achieved within the statistical framework. While it is known that the severity of the artifacts increases with the increasing angular range of the missing projections, limited-angle tomography does not provide information on which projections should be used in order to most effectively reconstruct the image.
Maximum likelihood (ML) estimation is a widely used method in the related art for reconstructing an image from a constrained set of measurements. A parameterization of the generative model described above is obtained by assigning an intensity I(u) to every voxel in U. The likelihood of the observed data y=(yt)t, given the set of parameters I={I(u):uεU} is:
Note that the lower and upper bound of an indexing variable (such as voxels u and time index t) are omitted in the following description, when they are clear from the context.
There is currently no analytic way to solve Eqn. 2 for the maximum of the likelihood function. However, optimization methods that find local maxima of the likelihood are known. One such method is the Expectation-Maximization (EM) process. In EM estimation, there is no guarantee that the sequence converges to a maximum likelihood estimator. For multimodal distributions, this means that an EM algorithm will converge to a local maximum (or saddle point) of the observed data likelihood function, depending on starting values.
Since the data generated by the model is only partially observable by our measurements, a basic ingredient of the Expectation-Maximization formalism is to define a set of random variables that completely define the data generated by the model. In the current case, since Yt=ΣuXt(u), the set of variables {Xu(t):uεU; t=1, . . . , T} is such a set; the generated data is x=(xt)t where xt=(xt(u))u, and the observed data y is completely determined by x. The main tool in the EM formalism is the complete data likelihood:
Since the likelihood depends on the complete data, which is only partially observable, we take its expectation with respect to the space of the unobserved data, given the current set of hypothesized parameters (i.e. the current estimator). The result is a function Q(I|I′) which assigns likelihood to sets I of model parameters, given the current set I′, and given the observed data y:
where C is a term which is independent of the intensities I. The function Q(I|I′) is maximized by the following new estimates:
The expectation in Eqn. 5 is obtained as follows:
It follows that E[xt(u)|yt;
and hence the EM iteration is:
It is provable that each EM iteration improves the likelihood. Thus, given a random starting estimator, the EM algorithm iterates the above improvement step until it converges to a local maximum of the likelihood. Several random starts increase the chance of finding a globally good estimator.
It is usually desired to maximize the expected posterior probability (given a proper prior) rather than the expected likelihood. In that case we assume a prior probability on the intensities P(I)=ΠuP(I(u)). A proper conjugate prior for the Poisson distribution is the Gamma distribution:
Now the maximization is done on Q(I|I′)=E[ ln P(x|I)p(I)|y; I′]. Plugging the Gamma prior into Q, and solving for I(u), we get the following EM iteration for the maximum posterior estimation:
The EM update step can be formulated in matrix notation as follows. Let Φ be the matrix of the projections [φl(u)]t,u, and let I, I′, y, α and β be represented as column vectors. Eqn. 10 can be written in vector and matrix notations as:
where the explicit multiplication and division denote element-wise operations, and where 1 is a vector (of the appropriate length) consisting solely of 1's.
Limited computational resources (i.e., when the entire projection matrix Φ cannot be kept in memory) may require breaking the update computation according to a partition of Φ into a set of sub-matrices (Φi). In that case the intensities can be updated gradually (using only one sub-matrix at each step) according to the following computation:
where yi is the vector of observations that are obtained using the views of Φi.
In the context of image reconstruction from a constrained set of views, the utility of the reconstruction algorithms described above is limited. Many estimation algorithms, including EM and the Radon transform, require measurements from a complete set of views surrounding the imaged object. Although algorithms for EM with missing views have been developed, these algorithms are based on equally spaced views surrounding the imaged object, of which a number of views are not available. These algorithms do not provide a generalized solution for an unconstrained set of views, which may not be equally spaced or available for all directions surrounding the object.
Singular value decomposition (SVD) is a known technique for factorizing a rectangular real or complex matrix, with applications in signal processing and statistics. SVD may be considered a generalization of Eigenvalue decomposition to m*n matrices, whereas Eigenvalue decomposition is applicable only to square matrices.
SVD states that given the m-by-n matrix M whose entries are either from the field of real numbers or the field of complex numbers, there exists a factorization of the form:
M=UDVT (13)
where U is an m-by-m unitary matrix, D is m-by-n with nonnegative numbers on the diagonal and zeros off the diagonal, and VT, the conjugate transpose of V, is an n-by-n unitary matrix. The elements along the diagonal of D are denoted the singular values. Such a factorization is called a singular-value decomposition of M. A common convention is to order the singular values Di,i in non-increasing fashion, so that the diagonal matrix D is uniquely determined by M.
The condition number of a matrix is defined as the ratio of the matrix's largest singular value to its smallest singular value. In numerical analysis, the condition number associated with a problem is a measure of that problem's amenability to digital computation. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. For example, the condition number associated with the linear equation x=My gives a bound on how accurate the solution y will be after approximate solution.
SVD may be employed for the solution of linear inverse problems. The inverse problem for a set of linear equations, x=My, is to calculate vector y from a known x and M. Using SVD, with M=UDV*, the problem may be restated as x=UDV*y. If D is an invertible matrix, y is obtained as:
y=VD−1UTx (14)
where U and Vt are unitary matrices, and D is a diagonal matrix containing the singular values of M. Since U and Vt are easily transposable, a solution to Eqn. 13 is obtainable only if D is invertible. As D is a diagonal matrix of singular values e1 to en (where ek denotes the k-th singular value Dk,k), D−1 is a diagonal matrix of the reciprocals of the singular values. That is:
If the dimension of y is larger than the dimension of x, y cannot be determined directly but rather can only be estimated, which is often performed by an iterative procedure. If the condition number of D is very large, the multiplicative factors ei−1 will vary greatly, thus multiplying any measurement or calculation errors based on individual or linear combinations of elements of y, and decreasing the likelihood of convergence of the iterative estimation procedure.
Truncated SVD is a known technique for reducing sensitivity to inaccuracies or noise when solving a set of linear equations. In truncated SVD, the constraints associated with the smaller singular values are eliminated from the estimation. In terms of the inverse problem of Eqn. 14, this is accomplished for the i-th singular value by setting equal to zero in matrix D−1. Thus the lower valued singular values no longer affect the estimation process.
In order to achieve a reconstructed image which is adequate for medical diagnostic and treatment purposes, a reliable, high-resolution image of the tested object (i.e. body structure) must be obtained. Currently, reliable reconstruction algorithms are available only for complete data sets, which provide coverage of the entire volume. Such data is generally not available during medical imaging. Additionally, when high-resolution detecting units are used, their efficiency is relatively low, and the detecting units must remain at each position for a relatively long time in order to achieve a high probability of detection. Since during medical testing, measurements are generally performed at many locations as the detecting unit is moved relative to the observed body structure, the testing procedure generally requires a long time and is physically and emotionally difficult for the patient. Additionally, reconstruction is based upon a large quantity of data, and is a lengthy and computationally complex process.
There is thus a widely recognized need for, and it would be highly advantageous to have, an apparatus, system and method devoid of the above limitations.
According to a first aspect of the present invention there is provided a method for stabilizing the reconstruction of an imaged volume. The method includes the steps of performing an analysis of the reliability of reconstruction of a radioactive-emission density distribution of the volume from radiation detected over a specified set of views, and defining modifications to the reconstruction process and/or data collection process to improve the reliability of reconstruction, in accordance with the analysis.
According to a second aspect of the present invention there is provided a reconstruction stabilizer, for improving the reliability of reconstruction of an imaged volume, according to a preferred embodiment of the present invention. The reconstruction stabilizer includes a reliability analyzer for performing an analysis of the reliability of reconstruction of a radioactive-emission density distribution of the volume from radiation detected over a specified set of views, and a modifier associated with the reliability analyzer, for defining modifications to at least one of a reconstruction process and a data collection process to improve the reliability of reconstruction, in accordance with the analysis.
According to a third aspect of the present invention there is provided a system for generating a three-dimensional image of volume, according to a preferred embodiment of the present invention. The system includes a radiological imaging camera comprising a plurality of detectors configured for independent movement during data acquisition, and configured for detecting radiation emitted from the volume thereby to provide radiation data, a reconstructor, configured for performing an analysis of the radiation data so as to reconstruct a three-dimensional image of the volume, and a reconstruction stabilizer associated with the camera and the reconstructor. The reconstruction stabilizer includes a reliability analyzer for performing an analysis of the reliability of reconstruction of a radioactive-emission density distribution of the volume from radiation detected over a specified set of views, and a modifier associated with the reliability analyzer, for defining modifications to at least one of a reconstruction process and a data collection process to improve the reliability of reconstruction, in accordance with the analysis, and for providing the modifications to at least one of the camera and the reconstructor.
According to a fourth aspect of the present invention there is provided a method of radioactive-emission measurements of a body structure, according to a preferred embodiment of the present invention. The method includes the steps of performing radioactive-emission measurements of the body structure, at a predetermined set of views, analyzing the radioactive-emission measurements, and dynamically defining further views for measurements, based on the analyzing.
According to a fifth aspect of the present invention there is provided a measurement unit for performing radioactive-emission measurements of a body structure, according to a preferred embodiment of the present invention. The measurement unit includes a probe for performing the radioactive-emission measurements of the body structure, where the probe is controllable to perform the measurements at a predetermined set of views, an analysis unit for analyzing the radioactive-emission measurements, and a view definer for dynamically defining further views for measurements, based on the analyzing.
The present invention successfully addresses the shortcomings of the presently known configurations by providing methods for stabilizing the reconstruction of an imaged volume and of performing radioactive-emission measurements of a body structure.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, suitable methods and materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting.
Implementation of the method and system of the present invention involves performing or completing selected tasks or steps manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of preferred embodiments of the method and system of the present invention, several selected steps could be implemented by hardware or by software on any operating system of any firmware or a combination thereof. For example, as hardware, selected steps of the invention could be implemented as a chip or a circuit. As software, selected steps of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In any case, selected steps of the method and system of the invention could be described as being performed by a data processor, such as a computing platform for executing a plurality of instructions.
The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
The invention is herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of the preferred embodiments of the present invention only, and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a fundamental understanding of the invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the invention may be embodied in practice.
In the drawings:
a-1i show detecting units and blocks of various geometries and constructions and radioactive-emission-measuring probes, associated with them.
j and 1k pictorially illustrate a view and viewing parameters associated with it, in accordance with definitions of the present invention.
a is a simplified flowchart of a method for stabilizing the reconstruction of an imaged volume, according to a preferred embodiment of the present invention.
b is a simplified flowchart of a method for analyzing a detection probability matrix, according to a preferred embodiment of the present invention.
c is a simplified block diagram of a reconstruction stabilizer, according to a preferred embodiment of the present invention.
d is a simplified flowchart of a method of performing radioactive-emission measurements of a body structure, according to a preferred embodiment of the present invention.
a illustrates an object having two high-emission regions of interest.
b illustrates the added information provided by each of views VA to VF.
a and 5b are simplified flowcharts of iterative methods of performing radioactive-emission measurements of a body structure, according to a first and a second preferred embodiment of the present invention.
a and 6b are simplified flowcharts of methods for dynamically defining further views, according to a first and a second preferred embodiment of the present invention.
a and 7b present the principles of modeling, for obtaining an optimal set of views, in accordance with the present invention;
a-9f show emittance models of a given volume to illustrate view selection using the separability criterion.
g-9i show emittance models of a given volume to illustrate view selection using a weighted-combination criterion.
The present embodiments teach providing modifications of the reconstruction and/or imaging processes in order to obtain a reliable reconstruction of the imaged volume. Specifically, the methods teach analyzing the reliability of the reconstruction obtainable from collected emission data over a set of views to determine modifications which are expected to improve reliability. The present embodiments further teach using radioactive-emission measurements to define views for further radioactive-emission measurements of a body structure, to be performed during the current measurement process.
With non-uniform scanning, the amount of information available for different voxels is not uniform, thereby constraining the ability to obtain an accurate reconstruction of the volume. In addition, there may be a need to focus on a region or regions of interest, and to control reconstruction resolution and accuracy where and when necessary. In such cases it is important to provide features and algorithmic components which handle or compensate for the lack of uniformity of information, and are capable of focusing on features or regions of interest, while maintaining short and efficient data acquisition.
In the context of medical imaging the imaged volume corresponds to a body structure, which may include a whole body, portion of a body, target organ and so forth. Those non-limiting embodiments presented below which are directed at imaging a body structure are to be understood as applying to any imaged volume.
Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting.
Referring now to the drawings,
Seen in
k schematically illustrates the emission rate of the volume U, as a function of time, given that a radioactive material of a specific half-life has been administered at a time T0.
A view may thus be defined as a group of nonzero probabilities of detecting a radioactive emission associated with all the voxels that form sector S (
A view is sometimes referred to as a projection, and the two terms are synonymous. Furthermore, a view defined over the sector S can be naturally extended to be defined over the group of all voxels in the volume U, by simply associating a zero probability with every voxel outside the sector S. This enables applying mathematical operations over the entire volume U.
The viewing parameters, which are the factors affecting the detection of radioactive emissions, are as follows:
i. Location and Orientation Parameters:
The half-life t1/2, of the radiopharmaceutical, the types of radioactive emission, whether gamma or beta, and the energies of the radioactive emission affect the probability of detection.
Some of these viewing parameters are fixed for a particular situation. Specifically, the tissue attenuation parameters are given. Additionally, the time t1 since administration of the radiopharmaceutical is generally governed by the blood pool radioactivity, since it is generally necessary to wait until the blood pool radioactivity dies out for low-level detection to be possible. For the remaining viewing parameters, optimization may be carried out.
To recapitulate the problem described above, an intensity distribution/, in terms of radioactive emissions per seconds, is defined over the volume U, forming our input space. Volume U comprises a set of basic elements u (e.g., pixels in two dimensional spaces, voxels in three dimensional spaces), and I(u) is the intensity in a given basic element uεU. A view (also denoted a projection) φεΦ is defined by the set of probabilities {φ(u):uεU}, where φ(u) is the probability of detecting a radioactive emission from a voxel u, as defined by viewing parameters, such as the physical and geometrical properties of the detecting unit, as well as the attenuation parameters of the viewed volume U, and the time parameters. A measurement is obtained by choosing a view φεΦ, and then sampling according to the viewing parameters.
As shown in Eqn. 1b, the relationship between the measurements, y, and the emission intensities over the body structure may be represented as y=Poisson(ΦI). The reconstruction problem we are faced with is to calculate the intensity vector I from the measurement vector y, given a known probability matrix Φ.
Applying SVD analysis to the probability matrix Φ, we obtain:
Φ=UDVt=>y=Poisson(UDVtI) (16)
where U and Vt are unitary matrices, and D is a diagonal matrix containing the singular values of Φ. Any destabilizing singular values in D are likewise destabilizing to the Poisson process. Specifically, those elements of I (or linear combinations of elements) for which insufficient data is available are equivalent, regardless of whether or not the photon emissions are modeled as Poissonian.
The following description is directed at a non-limiting preferred embodiment wherein the relationship between the measurements y and intensities I are modeled as a set of linear equations, y=ΦI, for the purposes of reconstruction. This model is suitable for least squares optimization when photon emissions have a Gaussian distribution, and thus may be reasonably applied when the measured counts (i.e. y) are relatively high. However the embodiments are extendable to modeling the emissions as Poissonian. In a preferred embodiment, when a given voxel or voxels are not within Gaussian range, the y values of several low-intensity views are combined and set equal to the sum of all the related linear equations, in order to bring the total count into Gaussian range.
Assuming intensities with a Gaussian distribution, then by applying SVD to the present inverse problem, I is obtained as:
I=VD−1Uty (17)
As discussed above, the condition number of D may serve as an indicator of the stability of the reconstruction, particularly during an iterative reconstruction process. Furthermore, known techniques such truncated SVD may be used for optimization and reconstruction purposes.
The present embodiments are of a method, apparatus, and system which analyze the reliability of the reconstruction possible by a given imaging constellation, and define modifications in order to improve the quality of reconstruction. The modifications may be to the reconstruction and/or data collection aspects of the imaging process. As described below, the modifications may use active view selection during imaging and/or to guide non-uniform scanning of the imaged volume.
Reference is now made to
The present embodiment tailors the reconstruction and/or data collections processes in order to obtain a more accurate reconstruction of the imaged volume. Low reliability data may cause large errors in the reconstruction process. As a result the reconstruction process may be noisy and unstable, and fail to converge properly. The reconstructed image may contain artifacts, unsupported frequencies and other errors.
The present embodiments are applicable to all stages of the imaging and/or reconstruction processes. The analysis may be performed prior to data collection, in order to define a scanning procedure which provides high-reliability data. During data collection, the scan pattern may be adapted or views may be added (e.g. active vision/adaptive scanning), utilizing the new information provided by the collected data. After data collection, modifications may be made to the reconstruction process in order to counteract the effects of unreliable data and non-uniformities, and to improve reconstruction accuracy and stability.
In a first preferred embodiment, the analysis of the reliability of reconstruction is based upon on analysis of the singular values of the probability matrix Φ. A non-limiting preferred embodiment of such an analysis is presented below.
Reference is now made to
In the preferred embodiment, a measure of the reconstruction reliability (denoted herein the reliability measure) is determined. The reliability measure is used for determining if any modification of the imaging and/or reconstruction processes is required, or if a stable reconstruction is possible without such modification.
Preferably, the condition number of the probability matrix is utilized as a reliability measure. If the condition number is satisfactory the reconstruction may be considered stable, with no need for modification. Preferably, the identifying of destabilizing singular values is performed only if the condition number is below a specified magnitude.
In an alternate preferred embodiment, the information-theoretic Fisher information is calculated as a reliability measure from intensity distributions provided of the imaged volume. An intensity distribution may be obtained either as an emittance model created prior to the data measurement process, or as an intermediate result of the reconstruction process. The Fisher information is described in detail below, in the context of the reliability criterion for active vision.
In the preferred embodiment, the identification of destabilizing singular values is performed as follows. The ratio of the largest singular value to each of the remaining singular values is calculated. A singular value for which the ratio is above a specified threshold is considered destabilizing. One may consider that if the effects of the destabilizing singular values upon the reconstruction are eliminated, the condition number of the detection probability matrix is effectively below the threshold.
Preferably, unreliable voxels or combinations of voxels associated with a given destabilizing singular value are identified. The intensity levels of such unreliable voxels or combination of voxels are unsupported in the collected emission data, due to the destabilizing effects of the associated singular value. Therefore the accurate reconstruction of such voxels and/or combinations is unlikely, and may destabilize the reconstruction process. The destabilization of the reconstruction by unsupported voxels may lead to artifacts and unsupported frequencies in the reconstructed intensities. These effects are not necessarily limited to the unsupported regions, but may extend into other portions of the volume and create artifacts there as well.
The voxels and linear combinations of voxels associated with a singular may be determined via SVD decomposition of the intensity distribution matrix Φ. The matrix V obtained by SVD decomposition of Φ indicates voxels or linear combinations of voxels whose intensity after reconstruction is most highly affected by each of the singular values in D. Each row of V indicates a weighting associated with a given singular value for each voxel in I. Consider the following example of a volume with four voxels i1-i4:
In a first example, assume that e4 is a destabilizing singular value, and that the fourth row of V, v4, equals [0.001 0.01 0.97 0.015]. Examining v4 it is seen that the coefficient for the single voxel i3 is significantly larger the coefficients of the other voxels. It is therefore quite apparent that the reliability of data regarding voxel i3 is particularly low, and it is unlikely that i3 can be accurately reconstructed. In this example, the preferred embodiment is to perform smoothing of i3 relative to the neighboring voxels. Smoothing may be a practical approach where an inaccuracy occurs in spatially localized regions of the volume. An exemplary criterion to determine which voxels should be smoothed, is to select voxels whose corresponding coefficient of vi is above a certain threshold.
In a second example, assume that e3 is a destabilizing singular value, and that the third row of V, v3, equals [0.5 −0.5 0.5 −0.5]. In the present example, the unreliability of the data relates to a combination of voxels which may be distributed over the volume, rather than to an independent, spatially located voxel or group of voxels. In the present example, the reliability of data regarding the linear combination 0.5i1−0.5i2+0.5i3−0.5i4, as reflected by measurements y, is low, which may lead to instability and inaccuracies during reconstruction. Since there are no dominant voxels it may be less effective to perform smoothing. Instead, the preferred embodiment is to constrain intensities of the combination of voxel intensities between iterations.
A proposed approach for applying such a constraint is as follows. Given a reconstructed intensity vector I′, modify the intensities prior to performing the next iteration as follows:
I′=>I′−vkα(vkTI) (18)
where vk is the row of V associated with a destabilizing singular number, ek, and α is a proportionality factor which may be related to the magnitude of ek. The effect of the voxel combination on the following iteration is therefore reduced as desired, where the reduction may be correlated with the dominance of the associated singular value.
Preferably, constraints are added during the reconstruction process to reduce or eliminate the effects of the unreliable data associated with destabilizing singular values.
In the preferred embodiment, the modifications include defining constraints on the reconstruction process. The reconstruction may be considered unreliable if one or more destabilizing singular values have been found, and the modifications may be made in order to reduce the effect of the destabilizing singular values upon the reconstruction. Examples of such constraints may include:
Smoothing a reconstructed image is performed by calculating the intensity level of a voxel based on the intensities of surrounding voxels, in order to control the magnitude and rate of the fluctuations in intensities between voxels. For example, the intensity of a given voxel may be corrected to better reflect its value as an average of the surrounding voxels. Smoothing may be performed over the entire volume, or only on portions of the volume deemed unreliable.
When a non-uniform scan is performed, it is possible that not all directions surrounding a voxel will have equal support. It may therefore be easier to distinguish voxel from some neighbors than from others. In the preferred embodiment, smoothing is performed directionally. In directional smoothing, the smoothing is weighted more strongly in certain directions than in others.
In a first example, directional smoothing is used to overcome the limitations of unreliable data by smoothing the voxel in the weaker directions. In a second example, a higher resolution is available for some portions of the volume than is available in other portions. If it is important to obtain a reconstruction having a uniform resolution, directional smoothing may be applied reduce the resolution in highly reliable portions of the volume to the resolution obtainable elsewhere.
A directional smoothing policy may be based on the Fisher information measure, which provides directionality information. The Fisher information matrix indicates directionality and cross-relationships between voxels, but may be difficult to calculate. In the preferred embodiment, a scalar Fisher information is calculated for groups of views, where each group is localized in a given direction. The scalar Fisher information measures may then be analyzed together, in order to determine the relationships between the different directions.
Low reliability voxels may be united or combined with surrounding voxels in order to increase their reliability. Voxels may combined by assigning the intensity level of a neighboring high-reliability voxel to the low-reliability voxel. Voxel merging may be carried out more extensively, by repeatedly merging the lowest reliability voxel with one of the neighboring voxels to form an aggregate of voxels, until no voxel is left with a reliability below a threshold. It will be appreciated that the aggregate voxels have a lower resolution locally, but all other regions with good coverage remain of high resolution, according to their coverage.
An opposite approach for high-reliability portions of the volume is to subdivide high-reliability voxels into smaller voxels in order to improve resolution while still achieving a required reliability. For example, if there are 1000 different views independently covering 1 cubic cm and almost not affected by the surrounding voxels, then theoretically that volume can be divided up to about 1000 voxels, if the views create a linearly independent set of equations with a good condition number.
A further possible modification of the reconstruction process may be to adjust the effect of certain unreliable voxels or linear combinations of voxels after each of one or more iterations of the reconstruction process. For example, the magnitude of unreliable voxels or combinations of voxels associated with a destabilizing singular value may be reduced towards zero or towards the value of neighboring voxels by a specified factor, possibly in proportion to their respective weightings in the associated row of matrix V and/or to the associated singular value.
An additional possible modification is to constrain the value of the input. For example, a realistic range of counts may be defined overall or per view based on view parameters, typical spatial structures and the like. Examples include adding a prior constraint such as a gamma distribution of intensities, a constant or piecewise-constant progression of intensities, a linear or piecewise-linear progression of intensities, smoothing or piecewise smoothing constraints, an intensity distribution based on the shape of or magnitude of the object being scanned (possibly determined during a pre-scan), or a maximal or known range of expected intensities,
The reconstruction process may be performed in a manner that obtains varying resolutions over the volume. In one approach, the entire volume is defined as a single huge voxel, and split over the reconstruction iterations to form smaller voxels. The process is performed repeatedly over all or some of the voxels of the volume, as long as the result of the split maintains a reconstruction reliability high enough for stable results.
In a further preferred embodiment, the information-theoretic Fisher information is used as a reliability measure. Modifications to the reconstruction and/or data collection processes may be performed when the Fisher information is deemed to be outside a specified range. The calculation of the Fisher information is described in detail below, in the context of the reliability criterion for active vision. The Fisher information may be calculated from the results of a previous reconstruction iteration, or, initially, from an emittance model provided of the imaged volume.
The following addresses a preferred embodiment in which the modification is implemented by defining views for imaging the volume. The defined views serve to guide the data collection process in order to obtain measurements which enable performing a stable and accurate reconstruction of the intensity distribution of the volume. In this manner, detecting resources may be invested effectively in order to improve reconstruction reliability. Scanning resources include, for example, detector dwell time, number of detectors, angular and translational increments, and the like—features that increase the amount of data collection.
Such modification may be performed when a region is interesting but is still left with coarse resolution, so as to allocate more scanning resources, such as dwell time, number of detectors, angular and translational increments, to cover that region and to form more independent views such as to increase the reliability of the reconstruction of that area. Preferably, the views are defined so as to obtained a desired resolution over the region of interest.
The defined views may yield a non-uniform scanning procedure. A scanning density may be specified by the angular and translational increment size, or steps, the smaller the increment, the higher the density. Additionally, the scanning density may be defined by the acquisition time at each position—the longer the time, the higher the density.
Non-uniform scanning may be defined by specifying varying scan densities for imaging the volume. For example, the modification may entail adjusting a local scanning density to scan a region of interest with high density, and to scan other regions with low density.
The non-uniform scans may relate to non-uniform angular steps of the detector along a sweep, non-uniform detector translational steps, or different steps by different detectors. Some detectors may employ dense steps and others may employ sparse steps, for example, based on active vision as taught hereinbelow.
The scan density may be adapted to the distance to the object of interest. Since resolution decreases with distance, the higher density may compensate for increased distance.
Additionally or alternatively, the angular steps may increase in density when scanning a region of interest, and decrease in density, when scanning other portions of the volume.
Furthermore, more than one region of interest may be scanned with dense steps, simultaneously. The two regions of interest may be, for example, a tissue region and a blood pool region. This has applicability, for example, to dynamic studies of blood perfusion, by providing even scanning resources both to the blood and to the tissue.
Additionally, convex scans may be employed.
Variable scans, where a same region is scanned first with a first density and then with another density, may be employed. Alternatively, a same region may be scanned by a first group of detectors with a first density and then by a second group of detectors with another density, concurrently, or at different times. Thus the same region is scanned with at some density by a given detector and at a different density by another detector.
In a further preferred embodiment, view definition is performed dynamically during radioactive-emission measurements of the volume. The definition of further views for measurement during the data collection process is denoted active vision herein and is described in detail below. Active vision may be performed independently or in conjunction with the present preferred embodiment of stabilizing the reconstruction of an imaged volume.
In the preferred embodiment, the method includes the further step of iteratively reconstructing the radioactive-emission density distribution of the volume, preferably by EM estimation. Reconstruction reliability is preferably evaluated after every iteration.
Reference is now made to
In the preferred embodiment, reconstruction stabilizer 140 is included in a system for generating a three-dimensional image of volume. In the preferred embodiment, the system further includes radiological imaging camera 155 and reconstructor 160. Camera 155 includes detectors capable of independent movement during data acquisition, and which are capable of detecting radiation emitted from the volume thereby to provide radiation data. In accordance with embodiments of the present invention, each block of the imaging camera construction or each detecting unit, where single-pixel detecting units are used, may be provided with at least one, and preferably, two, three, or as many as six degrees of motion such as, for example, rotational motion around the x, y, and z, axis, oscillatory motion about these axes, or translational motion along these axes. Camera 155 thus enables flexible view definition by modifier 150, increasing the likelihood that a reliable reconstruction will be achieved. Reconstructor 160 analyzes the radiation data provided by camera 155 so as to reconstruct a three-dimensional image of the volume.
Reconstructor stabilizer 140 guides camera 155 and reconstructor 160, by providing one or both with the modifications determined to improve reconstruction reliability.
In practice, it is generally necessary to reconstruct volumes at a high resolution (i.e. a large number of voxels) from many measurements. Implementing the techniques described above then requires the manipulation of extremely large matrices. The large size of these matrices poses difficulties both for performing the calculations and for memory management. These difficulties are particularly problematic when active view selection is performed.
In the preferred embodiment, calculations are performed in a localized manner. That is, calculations are performed for different sections of the volume in turn, progressing through the volume until it is covered in its entirety. When calculations are being made of a particular section of the volume, the variables relating to the other sections are “frozen”. Thus first a selected section of the volume may be stabilized, so that the reconstruction of following sections is based on data with improved reliability. Localized calculations, such as SVD decomposition, are performed on smaller sub-matrices rather than on a single large matrix, alleviating the difficulties of manipulating very large matrices.
The division of the volume into sections may be devised in any practical way, for example as sequential slices or by another spatial connection. The division may be based on the scan pattern, so that well-supported sections may be stabilized first, followed by less supported section. The division may also or alternately be based on knowledge of the body being imaged, such as its shape or composition. When imaging a body structure, the sections may be based on the known axes or structures of the organ
The following embodiments are of a method for determining further views for the imaging of a body structure, denoted active vision herein. Active vision addresses the problem of ensuring that the quality of data gathered during the measurement process is adequate to provide a high quality image. The collected data and/or the image reconstructed from the collected data is analyzed the while the measurement process is taking place. Based on the analysis, further views are defined. Since each view is associated with known values of the viewing parameter(s), selecting a view effectively specifies known viewing parameter values. The defined further views thus define a set of viewing parameter values, which are used during the current measurement process in order to collect data which yields a high-quality reconstruction of the body structure.
Active vision may be performed independently, as described in the embodiments presented below. Additionally or alternatively, active vision may be performed in conjunction with the above-described method for stabilizing reconstruction, by modifying data collection by dynamically providing additional views to improve reconstruction reliability (see
The following embodiments are not confined to a specific reconstruction algorithm. Further views are preferably defined based on one or more of the following:
Reference is now made to
Preferably the body structure is all or a portion of: a prostate, a heart, a brain, a breast, a uterus, an ovary, a liver, a kidney, a stomach, a colon, a small intestine, an oral cavity, a throat, a gland, a lymph node, the skin, another body organ, a limb, a bone, another part of the body, and a whole body.
In step 210 the radioactive-emission measurements are analyzed. Preferably the analysis includes one or more of:
In step 220, further views for measurements are dynamically defined, based on the analysis performed in step 210. Preferably, each of the views is associated with viewing parameters selected from the group consisting of: detector unit location, detector unit orientation, collection angle, and measurement duration. Defining a view consists of providing a value for each of the parameters associated with the given view. The analysis (step 210) and/or dynamic view definition (step 220) may take into account external parameters including: measurement duration, time elapsed from the administration of the pharmaceutical to the measurement, radiopharmaceutical half life, radioactive emission type, and radioactive emission energy.
Each of these analysis techniques, and their application to view definition, is now discussed in turn. While each of the analysis/view determination techniques is discussed as a separate embodiment, multiple techniques may be used together to obtain the desired image quality.
In a first preferred embodiment, a photon count analysis ensures that the photon count at a given view yields an acceptable measurement error. As discussed above, the radiative emissions of the body structure being imaged is a Poisson process. In a Poisson process the Poisson noise grows inversely to the square root of the number of photons detected. In other words, if N photons are collected from a given view, the resulting signal to noise ratio (SNR) equals:
SNR=n/√{square root over (N)}=√{square root over (N)} (19)
The unprocessed detector photon count at a given view thus provides significant information regarding the quality of the information obtained at a given view. If the photon count is too low, it may be desired to continue to collect photons at the current location/orientation in order to obtain a satisfactory SNR. Alternatively, it may be determined that enough photons have already been collected, and to terminate the current view and move on to the next view.
The analysis is preferably performed by defining a global or local required measurement error, and comparing the square root of the obtained photon count to the required measurement error. Photon count analysis can be applied to the current and/or previous views. When a photon count of a current view is found to be too low, the duration of the current view is preferably extended in order to obtain the required error value. When a photon count of a past view is found to be too low, an emission measurement at substantially the same location and orientation but having a longer duration than previously is preferably performed. Alternately or additionally, the collection angle at the given location/orientation is preferably increased.
In an additional preferred embodiment, a detector photon count is analyzed to identify detector saturation at a given view. Preferably, when a detector is determined to have saturated, a new view or views are selected to reinforce those views that have saturated. In an alternate preferred embodiment, further views are defined to avoid highly-radiating portions of the body structure.
In a second preferred embodiment, a photon collection rate at a given view is analyzed to determine if it is within a specified range. In the preferred embodiment, the photon count rate is used to identify regions of high or low interest. In prostate imaging, for example, a region of high interest may be identified by a high photon rate, indicative of a tumor. In a second example, a region of high interest may be identified in heart imaging by a low photon rate, indicative of non-functional tissues. After one or more areas of high and/or low interest are found, further views are preferably defined by selecting views to concentrate on regions of high interest and/or to avoid regions of low interest. It is thus possible to zoom in on a suspected pathology without repeating the emission measurement process.
In a further preferred embodiment, the analyzing of step 210 includes reconstructing a radioactive-emission density distribution of the body structure. Reconstruction may be performed according to any applicable technique known in the art. The reconstruction is then used as the basis for further analysis.
Reconstruction based on the data collected from the predetermined views provides information regarding the quality of information obtained from the preceding measurements, and which further views are likely to be most informative. Selecting new views based on reconstruction is intended to bring us into viewing from the more informative views or combinations of views.
Reference is now made to
a and 4b demonstrate how the proper selection of views may improve the quality of information obtained for the body structure, for example in distinguishing between two regions of interest within a given volume.
a illustrates an object 400 having two high-emission regions of interest (ROI), 410 and 420. For clarity the views VA to VF are shown as lines in
In simple terms, consider the object as having three regions: ROI 410 with intensity I1, ROI 420 with intensity I2, and a low-emission region 430 between the two ROIs with intensity I3. The detected intensity at a given detector is proportional to
where In is the emission intensity of region n and ri is the distance of region n from detector Vi.
b illustrates the added information provided by each of the shown views, VA to VF. Views VB and VC collect emissions from all three regions, and are therefore least informative. Views VD and VE collect emissions from only low emittance region 430, and therefore provide most information regarding the location of each ROI within the volume and the separation between ROIs 410 and 420. Views VA and VF pass only through a single ROI, and therefore provide an intermediate level of information. It is a goal of the present invention to determine, while the emission measurements of the body structure are taking place, that views in the vicinity of VD and VE are highly informative, and to add these further views to the measurement process.
A body structure reconstruction can be utilized in several ways to define further views. A first way is to identify interesting portions of the contour and structure of the reconstruction. For example, it is seen in
In a preferred embodiment, the reconstruction is analyzed to identify textural edges within the reconstruction, and view definition preferably includes selecting views at an angle to the textural edges. In the preferred embodiment, the angle is a substantially sharp angle in order to provide information regarding the edge.
In another preferred embodiment, the reconstruction is analyzed to identify volumetric boundaries within the reconstruction, and view definition preferably includes selecting views at an angle to the volumetric boundaries. It is expected that the defined views will provide information regarding the boundary and differences in surrounding tissues on either side of the boundary. In the preferred embodiment, the angle is a substantially sharp angle.
Another way to utilize the reconstruction to define further views is to identify suspected organ targets within the reconstruction, and to select further view(s) in close proximity to the suspected organ targets. A suspected organ target is typically detected by identifying portions of the reconstruction whose emission intensity distribution and spatial characteristics are typical of a suspect region.
In a first preferred embodiment, a suspected organ target is defined as a high-emittance portion of the reconstruction. In prostate imaging, for example, a suspected organ target may be a high-emittance portion of the structure, indicating a tumor. A high-emittance portion is characterized by an intensity that is greater than the background intensity by a factor of at least (1+α), where α is a parameter specified by the user. In practice, a hotspot is usually detectable only if the radiation levels within the hotspot are higher than the background level by a factor of 1.5-2. α is therefore typically defined between 0.5-1. However, the detectability of a hotspot rises as the radioactive intensity of the body rises, raising the photon count. Thus, a lower value of α may be used when the measured body structure is in a state of high-intensity emittance. For example, a body structure may be characterized by relatively high emittance immediately following the administration of the radiopharmaceutical, and be characterized by lower emittance at a later time.
In a second preferred embodiment, a suspected organ target is defined as a low-emittance portion of the reconstruction. In heart imaging, for example, a suspected organ target is defined as a low-emittance portion of the reconstruction, indicating non-functional tissues. A low-emittance portion is characterized by an intensity that is lower than the background intensity by a factor of at least (1+β), where β is a parameter specified by the user.
In the preferred embodiment the further views are used immediately for radioactive-emission measurements. The results of the new measurements are then used in another analysis to define new further views for additional measurements. The radioactive-emission measurements may then be said to be performed iteratively.
Reference is now made to
Reference is now made to
Referring again to
Preferably, analysis step 210 includes determining a resolution of the reconstruction. Resolution is preferably determined by analyzing the full width at half maximum (FWHM) of peak values of the reconstruction. The FWHM is given by the distance between points at which the reconstructions reaches half of a peak value. Preferably, further views are defined in step 220 to concentrate on the region for which higher resolution is required.
An additional way to define future views using the reconstruction is on an information-theoretic basis. A quality function expressing an information theoretic measure is defined. The quality function rates the information that is obtainable from the body structure when one or more permissible views are added to current measurement process. Several examples of quality functions based on information-theoretic measures are discussed in detail below. The quality function is used to rate potential further views. The measurement process may then continue at those further views whose addition to the previous views yields a high rating.
Reference is now made to
In the abovedescribed reconstruction-based analyses, the quality function is evaluated independently for a single reconstruction of the emission intensity of the body structure. However, quality functions may be defined which calculate the score for a given set in relation to one or more reconstructions and/or emittance models. An emittance model is a representation of a specific radioactive-emission intensity distribution within the volume U, so as to model organ targets, such as hot regions, of a radioactive emission intensity, higher than the background level, regions of low-level radioactive emission intensity, which is nonetheless above the background level, and cold regions, of a radioactive emission intensity, lower than the background level. Given an object or class of objects, emittance models may be devised to reflect expected or typical emission patterns for the given object.
Developing an emittance model for a particular body structure involves analyzing known information about the body structure to determine expected emission patterns of the body structure. In order to develop a model of a particular body structure, for example a prostate, many factors may be considered. Physical aspects, such as the size and shape of the prostate and the position of the prostate within the torso may be considered, as well as medical knowledge regarding typical emissions from healthy and diseased prostates. Additional information may concern variations between individuals, such as age, weight, percentage of body fat, and the like.
For simplicity, the following discussion describes the evaluation of information-theoretic quality functions based on emittance models only. It is to be understood that at least one of the emittance models is a reconstruction of the body structure based on past measurements. Any remaining emittance models are provided externally, and may be based on general medical knowledge or on information gathered during a previous round of emission measurements of the body structure.
Reference is now made to
Reference is now made to
It will be appreciated that the model 760 of the region of interest 730 may be based on general medical information of the body structure 740 and common pathological features associated with it. Additionally, the model may be based on information related to a specific patient, such as age, sex, weight, and body type. Furthermore, a structural image, such as by ultrasound or MRI, may be used for providing information about the size and location of the body structure 740 in relation to the body section 720, for generating the model 760.
Reference is now made to
In the preferred embodiment, one or more of the emittance models contains at least one high-emittance portion (i.e. hot region). A prostate containing a tumor, for example, may be modeled as an ellipsoid volume with one or more high-emittance portions.
In the preferred embodiment, one or more of the emittance models contains at least one low-emittance portion. A diseased heart may therefore be modeled as a heart-shaped volume with low-emittance portions.
Note that an emittance model need not contain high- or low-emittance portions, but may have a uniform intensity or a slowly varying intensity.
Following are two embodiments of quality functions, both of which include considerations of the emission distribution of the volume, in light of the emittance models provided (step 605 of
In a first preferred embodiment, the quality function implements a separability criterion. Separability is a measure of the extent to which the measurements that are obtained from each pair of models can be distinguished from one another.
The concept of separability is illustrated in
Letting I be the emittance model set, a measure for the dissimilarity of any two given densities in I is defined. Since most state-of-the-art estimating algorithm are aimed at finding ML estimators, in the current example the quality function is based on the likelihood function. The likelihood of an estimator of I, given a set of Poissonian measurements y is:
For separability, it is desired that this measure be different for each IεI. Since the measure is a random variable that depends on the actual measurements, all possible pairings of emittance models should be examined to ensure that the resulting distributions are separable. A quality function that captures this separability is given by the square of the difference between the means of the distributions normalized by the sum of their variances:
The expectations and variances in Equation 20 are taken over random measurements y, sampled from the true intensity I1 (note that the measure is not symmetric).
Since the true (unknown) intensity can be any IεI, a projection set Φ* that maximizes the worst-case separability is desired. That is:
Φ*=arg maxΦminI
Scoring for separability is based on the minimum separability obtained with a given set of views for all of the possible pairings of emittance models from the set of emittance models, thereby enabling defining a desired resolution in more than one direction, or in more than one portion of the volume. All of the emittance models are modeled on a substantially identical volume. The emittance models preferably differ from one another in the modeled organ targets, where the modeled organ targets are separated by a difference of at least the required resolution (where the displacement which produces the required resolution is denoted delta herein). Substantially identical sets of views are formed from the collection of views, and each of the formed sets is scored with respect to each of the pairs. One of the sets of views is selected, based on the minimum or average score for the plurality of pairs.
For example, assume the set of emittance models contains the three models 9a-9c. A separability score is calculated for a given formed set of views by applying Equation 20 to all three pairs 9a/9b, 9a/9c, and 9b/9c. The lowest of the three calculated values is taken as the separability score for the formed set. Once a separability score has been calculated in such manner for each of the formed sets of views, the view set having the highest separability is selected.
The separability criterion may be used to ensure that a required resolution is obtained in all or a portion of the body. In a preferred embodiment, view set selection for separability is performed utilizing a set of emittance models consisting of one pair of emittance models having substantially identical volumes but with different modeled organ targets. The modeled organ targets are separated by a delta in a given direction so as to define a required resolution in that direction and portion of the volume U. Substantially identical sets of views are formed from the collection of views, and scored with respect to the pair of emittance models, using a quality function based on the separability criterion, and one of the sets of views is selected based on the separability scores. The selected set is thus the set which provides the optimum resolution in the given direction and in the vicinity of the modeled organ targets.
A similar approach may be used to ensure resolution in more than one direction and/or portion of the volume U. Consider for example, a pair of models of substantially identical volumes, as follows: The model of
An optimal set of views, from the standpoint of separability, is that which will best distinguish between the model of
For example, consider the model of
Scores, in terms of separability, may be given to all the paring combinations, that is the models of
In a second preferred embodiment, the quality function implements a reliability criterion, which is a measure of how reliably the intensity distribution of a given object may be reconstructed from the sampled views. Since the input to the reconstructed algorithm is a random sample, the output estimator is also random. A desired property of this output is that it be reliable in the sense that similar estimators for different projected samples (i.e. different sets of measurements) of the same input intensity are obtained with high confidence.
The Fisher Information, Fφ(I) is a measure, known in the art, which is used to evaluate the expected curvature of the likelihood of a model/(taken over measurements sampled from the model I). The Fisher Information is defined as:
Fφ(I)=−E∇2L(I) (22)
The derivatives are taken with respect to the parameters of the intensity I, and the expectation is taken with respect to the random counts. Intuitively, a sharper curvature means that a maximum-likelihood estimation algorithm is more likely to produce a low-variance estimator. Indeed, this property is captured by the Cramer-Rao lower bound, which states that the inverse of the Fisher Information is a lower bound for the variance of any unbiased estimator, where an estimator f of the intensity I is unbiased if Ef(y)=I.
The Fisher information provides a value, FΦ(I)u,v, for each pair of voxels u and v. To provide a single measure for the reliability of the estimator, the average level, worst case, or other reasonable measure may be taken over the voxels. In the current example, the quality function is based on the average Fisher information. Starting with a set of emittance models to be used by the estimating algorithm to provide a reliable estimator, the average of the above measure is maximized over the entire set, defining the selected set Φ* as:
Alternately, a set may be chosen to minimize the inverse of the Fisher information, by selecting for:
Since inverting FΦ(I) may be computationally expensive, the [FΦ(I)−1]u,u term in Equation 24 may be replaced with 1/[FΦ(I)]u,u (thus neglecting the off-diagonal elements of the Fisher Information matrix FΦ(I)). Note that Equations 23 and 24 are not mathematically equivalent, and may therefore yield different selected sets.
In the preferred embodiment, evaluating the quality function is performed using the reliability criterion, and two or more emittance models are provided, having substantially identical volumes, but different modeled organ targets. Substantially identical sets of views are formed for all the emittance models, and each set is scored for reliability. One of the sets of views is then selected based on the average score for all the of the emittance models.
In a further preferred embodiment, a weighted combination of several information theoretic measures is used. For example, a plurality of models may be provided, all having substantially identical dimensions and volumes, as follows:
i. a pair of models with slightly different distributions of radioactive emission sources, as seen in
ii. a model with a given distribution of radioactive emission sources, as seen in any one of
Identical sets of views may be applied to all the models, and each view may be scored in terms of separability and reliability. An optimal set of views may be selected based on a summation of the two scores, or based on a weighted average of the two scores, where the relative weight given to each criterion reflects the relative importance of each measure per the given application.
The quality function is preferably defined in accordance with one of the following: worst case effectiveness for the given further view over the volume, average effectiveness for the given further view over the volume, worst case effectiveness for the given further view over the set of emittance models and average effectiveness for the given further view over the set of emittance models.
Maximization of the quality function may be performed utilizing any method known in the art such as simulated annealing and gradient ascent. In the simulated annealing (SA) method, each point of the search space is compared to a state of some physical system. The quality function to be maximized is interpreted as the internal energy of the system in that state. Therefore the goal is to bring the system from an arbitrary initial state to a state with the minimum possible energy.
The neighbors of each state and the probabilities of making a transition from each step to its neighboring states are specified. At each step, the SA heuristic probabilistically decides between moving the system to a neighboring state s′ or staying put in state s. The probabilities are chosen so that the system ultimately tends to move to states of lower energy. Typically this step is repeated until the system reaches and acceptable energy level.
Gradient ascent, on the other hand, is based on the observation that if a real-valued function F(x), such as the quality function of the present embodiments, is defined and differentiable in a neighborhood of a point a, then F(x) increases fastest if one goes from a in the direction of the gradient of F at a, ∇F(a). It follows that if:
b=a+γF(a) (25)
for γ>0 a small enough number, then F(a)≦F(b). Gradient ascent starts with a guess x0 for a local maximum of F, and considers the sequence x0, x1, x2, . . . such that:
xn+1=xn+γ∇F(xn), n≧0. (26)
Since F(x0)≦F(x1)≦F(x2)≦ . . . , the sequence (xn) is expected converges to a local maximum.
Preferably, the set of views selected with the quality function is increased by at least one randomly selected view. The randomly selected view(s) increase the probability that the quality of information obtained with the further views is maximized globally rather than locally.
As discussed above, selecting the best set of size N from amongst a large set of candidate projections is computationally complex. Since the size of the collection of views and of the required set may be large, a brute force scheme might not be computationally feasible.
In an additional preferred embodiment, a so-called “greedy algorithm” is used to incrementally construct larger and larger sets, until the required number of further views is defined. When multiple further views are required, it is computationally complex to maximize the quality function over all possible combinations of further views. The greedy algorithm reduces the computational burden by selecting the further views one at a time. The algorithm starts with a current set of views, and for each iteration determines a single view that yields the maximum improvement of the set score (hence the name “greedy”).
In theoretical terms, assume ρ(•) is the quality measure we are using for the view selection, and assume without loss of generality that we are trying to maximize this measure. We gradually build a set W of projections as follows. We start with an empty set W=Ø, and at every stage choose the projection that maximizes the quality measure when added to the current set:
W←arg maxW′{ρ(W′)|W′=W∪{φ},φεΦ} (27)
In other words, during a given iteration, a respective score is calculated for a combination of the previous set with each of the views which is not a member of the current set. The current set is then expanded by adding the view which yielded the highest respective score, and the expanded current set serves as the input to the following iteration. Thus the number of times the scoring function is calculated per iteration drops from iteration to iteration. For a large collection of possible views, the greedy algorithm reduces the total number of computations required for set selection.
Reference is now made to
Reference is now made to
Reference is now made to
In step 1220 at least one quality function is provided. Each quality function is for evaluating sets of views, essentially as described above. A single quality function may be used to select several sets of views, where each set of views contains a different number of views.
In step 1230, multiple sets of further views (where a set may include a single further view) are formed from the collection of views, using the quality function(s) provided in step 1220. In a first preferred embodiment, each of the sets is formed using a different one of the quality functions. In an alternate preferred embodiment, one or more of the quality functions are used to form more than one set of views, where sets formed with the same quality function have differing numbers of views.
In step 1240, a selected set of views is obtained from the sets formed in step 1230.
In a first preferred embodiment, the final set of views is obtained by choosing one of the sets formed in step 1230 using a set selection criterion. For example, a respective set is formed in step 1230 for the separability and reliability criteria independently. A set selection criterion which calculates an overall performance rating for a given set taking both criteria into account is defined, and the formed set with the highest overall rating is selected as the final set.
In another preferred embodiment, the selected set of views is obtained by merging the sets formed in step 1230 according to the relative importance of the respective quality function used to form each set.
In the preferred embodiment, the method further consists of providing at least one emittance model and/or reconstruction representing the radioactive-emission density distribution of the volume, and of evaluating with at least one of the quality functions of step 1220 is performed in relation to the emittance models.
As discussed above, since each view is associated with one or more parameters, the selected set yields a group of parameter values for performing effective detection of the intensity distribution of the body structure. For example, if each view is associated with a view location parameter the selected set defines a set of locations for collecting emission data from an object, in order to provide a high-quality reconstruction of the intensity distribution of the body structure.
Reference is now made to
The abovedescribed methods for radioactive-emission measurements of a body structure begin by performing measurements at a predetermined set of views. The results of the initial measurements are then analyzed and further views are defined.
The initial set of views is preferably selected based on information theoretic measures that quantify the quality of the data fed to the reconstruction algorithm, in order to obtain the best data for reconstructing a three-dimensional image of the body structure.
In accordance with the present invention, our approach is delineated by the following process:
The following section concentrates on the second step of the process, namely, obtaining the optimal and permissible set of initial views for performing the radioactive-emission measurements of the body structure. The initial predetermined set of views is denoted herein the optimal set of views.
We consider here the following problem: Assume that there is a large pool of candidate views to choose from, but due to time restrictions or other restrictions we are limited to a specific number of views N. Which are the best N projections in terms of the quality of the reconstruction? It is further assumed that the pool of projections may be constrained, and hence general sampling theorems (e.g., Radon Transform) cannot be applied. For instance, we consider a scenario in emission tomography where the detecting unit can be located on top of one face of a given volume but not on the others. In such cases, methods such as EM estimation do not clearly establish what is the best scanning scheme, in order to provide the best reconstruction of the radioactive intensity distribution of the volume.
Reference is now made to
The view set is preferably tailored to correspond to the actual limitations and constraints likely to be encountered when collecting data for a given object, that is a given body structure. For example, in medical applications the detecting unit can generally view the body structure only from certain distances and orientations, which are determined by the patient's anatomy and the structure of the probe. The view set may therefore be designed to contain views having only those viewing parameter values consistent with attainable distances and orientations. The view set may also be designed to contain views having only those viewing parameter values suitable for a given measurement scenario, for example having identical values for the type of radiopharmaceutical and time since administration.
Preferably, the collection of views represents a quantized continuum of views. The view collection thus reflects the detection probability distribution for a detecting unit making periodic measurements while moving along a trajectory.
Reference is now made to
During data collection, the probability of detection for each voxel is dependent on the parameters outlined above. In the preferred embodiment, a respective projection is calculated for each view, giving the view's detection probability distribution (i.e. the detection probability for each voxel of the volume). For a given view, the associated projection will have significant detection probabilities only for those voxels within the sector defined by the detecting unit's collection angle and location and orientation, as illustrated in conjunction with
The detection probability distribution for each view, that is the group of probabilities for each voxel, for a given view, is calculated according to techniques known in the art for determining the detection probability of a radioactive emission from a given voxel, under the constraints specified by the viewing parameters, for example, based on computer simulations of the geometry and the other viewing parameters, delineated hereinabove.
Generally, more distant voxels will have a lower probability of detection than closer voxels along the same line of sight. The volume attenuation coefficient may be constant or may vary over the volume. Thus, different sets of views may be produced for a single sector, by defining volumes with differing attenuation coefficients. For example, bone tissue and muscle tissue have different attenuations. Anatomical knowledge of the body structure being imaged may be used to develop a model of the volume U with a non-uniform attenuation that reflects the expected attenuation of the given body structure.
Referring again to
In step 1425, sets of views are formed from the collection of views. A score is then calculated for each of the sets.
In step 1430, the scores calculated in step 1425 are used to select one of the formed sets of views as the optimal set of views for the abovedescribed methods of performing radioactive-emission measurements of a body structure. A given scoring function may be used to select a set in a number of ways. In a first preferred embodiment, a required number of views is specified, and the highest scoring set with the specified number of views is selected. In a second preferred embodiment, the user may specify a minimal score which is known to provide satisfactory information quality, and select the smallest set which provides the specified score. However given a large collection of views the required number of calculations may be prohibitive. A third preferred embodiment used to reduce the computational burden is the greedy algorithm embodiment, similar to the abovedescribed method of
As discussed above, the scoring function is a measure of the quality of information which may be gathered for the volume using the given set of views. Both the separability and reliability criteria discussed above may be utilized as scoring functions, substantially as described above.
In an additional preferred embodiment, the scoring function implements a uniformity criterion, to ensure uniform coverage of the volume. It is often desired to obtain a uniform reconstruction quality among a given set of voxels W⊂U, where W is the set of voxels for which it is desired to obtain uniform detection. Note that by selecting the appropriate W, the uniformity criterion is applied to all or a portion of the body. The uniformity criterion ensures that the spread of the total influence of each element on the set of measurements is as uniform as possible. The uniformity criterion depends only on the collection of views Φ and requires no assumptions on the distribution I.
For a set Φ of projections, the total influence of an element, u, is given by ΣφεΦφ(u). Normalizing these values to PΦ(u), such that
a probability measure is obtained for which the entropy H(Φ) can serve as a uniformity measure:
The selected set Φ* is the set (containing the required number of views) that satisfies:
Φ*=arg maxΦH(Φ) (29)
Reference is now made to
Assume that the probabilities of detection are as follows:
Consider two possible sets of views: set {A, B, C} and set {B, C, D}. For set {A, B, C}, the total contribution of voxel 1610 is 0.8 (0.6+0.2+0) and of voxel 1620 is 0.8 (0+0.5+0.3). Normalizing these values for set {A, B, C} gives a probability set of [0.5,0.5]: For set {B, C, D}, the total contribution of voxel 1610 is 0.2 (0.2+0+0) and of voxel 1620 is 0.9 (0.5+0.3+0.1). Normalizing these values for set for set {B, C, D} gives a probability set of [0.18,0.82]. Thus:
H({A,B,C})=−(0.5*log2 0.5+0.5*log2 0.5)=−(−0.5−0.5)=1
H({B,C,D})=−(0.18*log2 0.18+0.82*log2 0.82)=−(−0.44−0.07)=0.51
Set {A, B, C} is thus seen to provide a more uniform coverage of volume 1600 than set {B, C, D}.
In an additional preferred embodiment, the greedy algorithm is used to incrementally construct larger and larger sets, until a set containing the required number of views is obtained. As described for
In a further preferred embodiment of a method for the selection of an optimal set, multiple view sets are first formed from one or more scoring functions, and then a final selection is made of one of the resulting sets, substantially as described for
The abovedescribed methods may each be embodied as a computer program stored on a computer-readable storage medium. In the preferred embodiment, computer-readable storage medium contains a set of instructions for defining views for radioactive-emission measurements of the body structure. An analysis routine analyzes the radioactive-emission measurements obtained from a radioactive-emission-measuring probe, and a view definition routine dynamically defines further views for measurements, based on the analyzing.
The active vision embodiments discussed above may be provided as modifications to improve reconstruction reliability. Reference is now made to
The above-described improved reconstruction reliability and active vision techniques enable high-quality reconstruction based on data collected from a limited collection of views. The ability to improve reconstruction reliability, both before and during imaging, reduces the need for repeated imaging to obtain additional measurements. Reconstructing the intensity distribution from a smaller quantity of collected data utilizing a stable reconstruction process simplifies the computational process. Furthermore, these methods enable resolving the current conflict between the relatively large-pixel detectors needed for measurement speed and data processing considerations, with the small-pixel detectors needed until now to obtain a high-resolution reconstruction. The abovedescribed embodiments are particularly suitable for medical imaging purposes, where a high-resolution image is needed and it is desired to minimize the difficulties of the patient undergoing the diagnostic testing or treatment.
This application claims the benefit of:
This application further incorporates by reference all the information of the International Application entitled “Imaging Protocols” which is being co-filed by the same assignee of the present invention on Jul. 19, 2006.
It is expected that during the life of this patent many relevant detection probes, detector types, radiation-based detection systems, algorithms for reconstruction and analyzing the reliability of reconstruction, and algorithms will be developed and the scope of the corresponding terms are intended to include all such new technologies a priori.
It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination.
Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 171346 | Oct 2005 | IL | national |
| 172349 | Nov 2005 | IL | national |
This application is a continuation of U.S. patent application Ser. No. 11/988,926 filed on Feb. 5, 2009, which is a National Phase of PCT Patent Application No. PCT/IL2006/000840 having International Filing Date of Jul. 19, 2006, which claims the benefit of priority of U.S. Provisional Patent Application Nos. 60/816,970 filed on Jun. 28, 2006, 60/800,846 filed on May 17, 2006, 60/800,845 filed on May 17, 2006, 60/799,688 filed on May 11, 2006, 60/763,458 filed on Jan. 31, 2006, 60/750,597 filed on Dec. 15, 2005, 60/750,334 filed on Dec. 15, 2005, 60/750,287 filed on Dec. 13, 2005, 60/741,440 filed on Dec. 2, 2005,60/720,652 filed on Sep. 27, 2005, 60/720,541 filed on Sep. 27, 2005, 60/720,034 filed on Sep. 26, 2005, 60/702,979 filed on Jul. 28, 2005, 60/700,753 filed on July 20; 2005, 60/700,752 filed on Jul. 20, 2005, 60/700,318 filed on Jul. 19, 2005, 60/700,299 filed on Jul. 19, 2005 and 60/700,317 filed on Jul. 19, 2005. PCT/IL2006/000840 is also a Continuation-in-Part of PCT Patent Application Nos. PCT/IL2006/000562 filed on May 11, 2006, PCT/IL2006/000059 filed on Jan. 15, 2006, PCT/IL2005/001215 filed on Nov. 16, 2005 and PCT/IL2005/001173 filed on Nov. 9, 2005. PCT/IL2006/000840 claims the benefit of priority of Israel Patent Application Nos. 172349 filed on Nov. 27, 2005 and 171346 filed on Oct. 10, 2005. The contents of the above Applications are all incorporated herein by reference.
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