Patent Application
20200085397
The present invention relates to an attenuation coefficient image estimation method, an attenuation coefficient image estimation program, a positron CT apparatus equipped with the same, which estimate an attenuation coefficient image from measurement data of a positron CT apparatus (positron emission tomography).
A positron CT apparatus, i.e., a PET (Positron Emission Tomography) apparatus, is configured to measure two γ-rays generated by positron annihilation regarded as valid signals only when they are simultaneously detected by a plurality of detectors (that is, only when they are coincidentally counted), and the tomographic image of the subject is reconstructed based on the measurement data. Specifically, a radioactive pharmaceutical containing positron emitting nuclides is administered to a subject, the 511 keV annihilation γ-rays emitted from the administered subject are detected by detectors composed of a number of detector elements (e.g., scintillators). And, when γ-rays are detected within a fixed time period with two detectors, it is regarded as being detected “coincidentally”, they are counted as a pair of annihilation γ-rays, and furthermore, a straight line (LOR: Line Of Response) connecting two detectors that detected the annihilation occurrence positions is specified. The coincidence counting information detected as described above is accumulated and subjected to reconstruction processing to obtain a positron emitting nuclide image (i.e., a tomographic image).
In a positron CT (PET), in order to perform a quantitative measurement of a radioactivity concentration in a subject, various data correction processing are required. Representative correction processing include sensitivity correction, scatter correction, random correction, decay correction, dead time correction, and attenuation correction. The present invention relates to an attenuation correction for preventing a decrease in image quantitative performance due to the attenuation of γ-rays emitted from a radioactive pharmaceutical (radioisotope). In order to perform an attenuation correction, it is necessary to estimate an attenuation coefficient image representing an attenuation coefficient distribution in a subject.
In the attenuation correction, the transmittance of γ-rays is obtained from the estimated attenuation coefficient image, and the measurement data of PET is divided by the transmittance to convert into data from which the influence of the attenuation of γ-rays has been eliminated. Alternatively, the estimated attenuation coefficient image is incorporated into the calculation formula of the image reconstruction to obtain a reconstructed image from which the influence of the attenuation of γ-rays has been eliminated.
In order to estimate the attenuation coefficient image, transmission data obtained by irradiating the positron-emitting nuclide with the external radiation source is needed. Alternatively, it is possible to estimate the attenuation coefficient image by using CT data obtained from an X-ray CT (Computed Tomography) apparatus instead of transmission data.
In recent years, there is a reconstruction algorithm that does not require such transmission data (see, for example, non-Patent Documents 1 and 2). In non-Patent Documents 1 and 2, from the measurement data of PET measuring the detection time difference (TOF: time-of-flight) information of the annihilation radiation (hereinafter referred to as “TOF-PET”), it is possible to estimate the distribution shape of the attenuation coefficient sinogram. The radioactivity image and the attenuation coefficient sinogram can be estimated simultaneously. The reconstruction algorithm in non-Patent Documents 1 and 2 is also called “simultaneous reconstruction algorithm” because it simultaneously estimates the radioactivity image and the data regarding attenuation coefficient (for example, attenuation coefficient sinogram). In particular, the simultaneous reconstruction algorithm that simultaneously estimates the radioactivity image and the attenuation coefficient sinogram is referred to as an MLACF method.
The principle of the MLACF method will be described qualitatively with reference to the conceptual diagram of
If there is no γ-ray attenuation, restoring the two-dimensional distribution per projection angle θ enables conversion into the original radioactivity distribution. However, in practice, a radioactivity distribution different from the original radioactivity distribution is restored due to γ-ray attenuation. Also, the degree of attenuation of γ-rays differs depending on the projection direction. As shown in
However, only the distribution shape (that is, the relative value) can be estimated, and the absolute value cannot be estimated. If the absolute value of the attenuation coefficient sinogram is not known, the attenuation correction cannot be performed correctly. Therefore, a quantitative radioactivity image cannot be obtained. This is problematic in clinical situations and becomes a major barrier to practical use.
In order to put the PET imaging technology based on the simultaneous reconstruction algorithm into practical use, the following technology is indispensable. That is, a technique for estimating an attenuation coefficient image in which the absolute value is correct from an attenuation coefficient sinogram in which the distribution shape is correct but the absolute value is incorrect.
Therefore, as a conventional technique of non-Patent Document 2, there is a method of directly quantifying a radioactivity image without directly quantifying an attenuation coefficient sinogram. The processing step is as follows.
(1) a radioactivity image with no attenuation correction is generated, and a subject mask image is generated from the radioactivity image.
(2) a known attenuation coefficient (for example, an attenuation coefficient of water or an attenuation coefficient of a bone) is substituted for each pixel value of the subject mask image, and a pseudo attenuation coefficient image is generated.
(3) a radioactivity image is generated by a conventional reconstruction algorithm using a pseudo attenuation coefficient image, and a total pixel value is calculated for each slice along axial direction. As shown in
(4) a non-quantitative radioactivity image and a non-quantitative attenuation coefficient sinogram are estimated by a simultaneous reconstruction algorithm.
(5) in the same manner as in Step (3), the total pixel value is calculated for each axial direction slice of the non-quantitative radioactivity image obtained in Step (4). Here, S′(z) is the total pixel value for each axial direction z slice.
(6) the non-quantitative radioactivity image obtained in Step (4) is scaled and quantified so that the total pixel value S′(z) obtained in Step (5) and the total pixel value S(z) obtained in Step (3) coincide with each other for each axial direction slice. Specifically, the radioactivity image is scaled by multiplying each pixel value of the non-quantitative radioactivity image obtained in Step (4) by S(z)/S′(z) for each axial direction slice.
Non-Patent Document 1: A. Rezaei, M. Defrise and J. Nuyts, “ML-reconstruction for TOF-PET with simultaneous estimation of the Attenuation Factors”, IEEE Trans. Med. Imag., 33 (7), 1563-1572, 2014
Non-Patent Document 2: V. Y. Panin, H. Bal, M. Defrise, C. Hayden and M. E. Casey, “Transmission-less Brain TOF PET Imaging using MLACF”, 2013 IEEE Nuclear Science Symposium and Medical Imaging Conference, Seoul, Republic of Korea, 2013.
However, in the prior art of Non-Patent Document 2 described above, there is a problem that it cannot be guaranteed in principle that the finally obtained radioactivity image is quantitative.
The present invention has been made in view of the above-described circumstances, and aims to provide an attenuation coefficient image estimation method, an attenuation coefficient image estimation program, and a positron CT apparatus equipped with the same, which are capable of generating a quantitative attenuation coefficient image.
The inventor has obtained the following findings as a result of earnest studies to solve the above problems.
That is, the above-mentioned prior art assumes that the total pixel value for each axial direction slice obtained in the above-described Step (3) is true (that is, it is correct).
However, there is no guarantee that the total pixel value for each axial direction slice obtained in the above-described Step (3) is correct. Since the quantification is based on the result in which there is no correct guarantee, naturally, the quantitative accuracy of the radioactivity image obtained in the above-described Step (6) cannot be guaranteed. Therefore, the problem arises that the prior art cannot generate a quantitative radioactivity image. That is, the inventor has found that the root of the problem of the prior art is based on an empirical method and is not based on a mathematical theory behind the problem of quantification of the attenuation coefficient.
The present invention based on such findings has the following configuration.
That is, an attenuation coefficient image estimation method according to the present invention is an attenuation coefficient image estimation method of estimating an attenuation coefficient image from measurement data of a positron CT including time-of-flight information of annihilation radiation. The method includes:
a reconstruction calculation step of calculating an image based on optimization of an evaluation function regarding the measurement data, wherein is an image in which a non-uniform offset value is added to a quantitative attenuation coefficient image;
a mask calculation step of calculating subject mask projection data which is subject mask data in projection data space based on the measurement data;
an offset estimation step of estimating an offset image μoff by a reconstruction algorithm configured such that forward projection data of the offset image μoff approximates the subject mask projection data, where μoff is a non-uniform offset image;
a reference region extraction step of extracting at least one or more regions Ω using an image in which a subject region is recognizable calculated based on the measurement data, wherein Ω is a region capable of being approximated by a known attenuation coefficient value;
a coefficient calculation step of calculating a which reduces an error between a value of the image μ′ in the region Ω and the known attenuation coefficient value, wherein α is a coefficient; and
an attenuation coefficient value correction step of correcting a value obtained by adding α×μoff obtained by multiplying the offset image μoff by the coefficient α to the value of the image μ′ as an attenuation coefficient value.
According to the attenuation coefficient image estimation method of the present invention, in the reconstruction calculation step, based on the optimization of the evaluation function regarding the measurement data (measurement data of TOF-PET) of the positron CT in which the time-of-flight information of the annihilation radiation is included, an image in which the non-uniform offset value is added to the quantitative attenuation coefficient image is calculated. At the same time, when λ′ is a non-quantitative radioactivity image, the radioactivity image λ′ is calculated in the reconstruction calculation step. The reconstruction algorithm in the reconstruction calculation step here is the simultaneous reconstruction algorithm described above. Here, when an image in which a non-uniform offset value is added to a quantitative attenuation coefficient image is μ′, the image μ′ also becomes an attenuation coefficient, but is simply referred to as an “image μ” in distinction from the quantitative attenuation coefficient image to be finally obtained.
On the other hand, in the mask calculation step, subject mask data in the projection data space (hereinafter referred to as “subject mask projection data”) is calculated based on the measurement data. When μoff is a non-uniform offset image, in the offset estimation step, an offset image μoff is estimated by the reconstruction algorithm configured such that the forward projection data of the offset image μoff approximates the subject mask projection data.
On the other hand, when Ω is a region that can be approximated by a known attenuation coefficient value, using the image in which the subject region is recognizable calculated based on the measurement data, in the reference region extraction step, at least one region Ω is extracted.
Here, the “an image in which the subject region is recognizable calculated based on measurement data” is, for example, the image μ′ mentioned above, the radioactivity image λ′ mentioned above, the non-quantitative image estimated by the reconstruction algorithm different from the reconstruction algorithm (simultaneous reconstruction algorithm) in the reconstruction calculation step mentioned above, and the subject mask image estimated from the subject mask projection data mentioned above. Of course, the image is not limited to the exemplified images, and may be any image in which the subject region is recognizable calculated based on the measurement data. Further, “extracting at least one or more regions Ω using an image in which a subject region is recognizable calculated based on the measurement data” includes not only extracting the region Ω using a single piece of image information, but also extracting the region Ω using a combination of a plurality of pieces of image information (for example, logical sum or logical product).
The following coefficient calculation step and attenuation coefficient value correction step are performed using the images μ′, the offset image μoff, and the region Ω obtained in the above-described steps. When μ is an unknown true attenuation coefficient image value (attenuation coefficient value) and α is a coefficient, in the coefficient calculation step, a coefficient α that reduces the error between the value of the image μ′ in the region Ω and a known attenuation coefficient value is calculated. In the attenuation coefficient value correction step, the value obtained by adding α×μoff obtained by multiplying the offset image μoff by the coefficient a to the value of the image μ′ is corrected as an attenuation coefficient value. In this way, the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α (i.e., μ≐μ′+α×μoff). Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables accurate attenuation correction of the radioactivity image.
The above-mentioned reconstruction calculation step may be performed by (a) a calculation algorithm in which the image μ′ is included as an unknown variable. Alternatively, the above-mentioned reconstruction calculation step may be performed by (b) a combination of a calculation algorithm in which attenuation coefficient projection data is included as an unknown variable and an algorithm in which an image obtained by reconstructing the attenuation coefficient projection data is set as the image μ′.
The former algorithm (a) is an MLAA method that simultaneously reconstructs the non-quantitative radioactivity image λ′ and the image (non-quantitative attenuation coefficient image). The latter algorithm (b) is a combination of the MLACF method described in non-Patent Document 1 which simultaneously estimates the non-quantitative radioactivity image λ′ and the non-quantitative attenuation coefficient projection data (e.g., attenuation coefficient sinogram) and an algorithm in which the image obtained by reconstructing the attenuation coefficient projection data is set as the image μ′. The algorithm in which the image obtained by reconstructing the attenuation coefficient projection data is set as the image μ′ in the latter (b) is not specifically limited, and may be any algorithm as long as it is a reconstruction algorithm.
An example of the mask calculation step mentioned above includes a step of calculating the binarized image of the image as a subject mask image, a step of calculating the projection data of the subject mask image, and a step of calculating the binarized data of the projection data of the subject mask image as a subject mask projection data (Aspect (A)). Further, the mask calculation step mentioned above includes a step of calculating the projection data of the image μ′ and a step of calculating the binarized data of the projection data of the image μ′ as a subject mask projection data (Aspect (B)). In the above aspect (A), the projection data is calculated after binarizing the image μ′ first, and the projection data is binarized. In the above aspect (B), the projection data of the image μ′ is first calculated and then binarized. The image μ′ is an attenuation coefficient image that is not quantitative, but subject mask projection data can be calculated even if by binarizing the image other than the attenuation coefficient image or the projection data.
Another example of the mask calculation step includes the step of calculating binarized data obtained by converting the measurement data of TOF-PET described above into the projection data format and binarized it as subject mask projection data. In the case of this example, the data converted into the projection data format and binarized can be calculated as the subject projection data directly using the TOF-PET measurement data.
Further, another example of the mask calculation step includes a step of calculating a radioactivity image based on optimization of an evaluation function regarding the measurement data of (the above-described) TOF-PET, a step of calculating projection data of the radioactivity image, and a step of calculating data obtained by binarizing the projection data (of the radioactivity image) as the subject mask projection data (Aspect (C)). Further, the mask calculation step includes a step of calculating a radioactivity image based on optimization of an evaluation function regarding the measurement data of (the above-described) TOF-PET, a step of calculating a binarized image of the radioactivity image, a step of calculating projection data of the binarized image, and a step of calculating data obtained by binarizing projection data of the binarized image as the subject mask projection data (Aspect (D)). In the above aspect (C), the binarization is performed after the projection data of the radioactivity image is first calculated. In the above aspect (D), the projection data is calculated after binarizing the radioactivity image first, and the projection data is binarized. In any of the above aspect (C) and the above aspect (D), in the case of this example, the reconstruction algorithm for calculating the radioactivity image is not particularly limited. When the above-mentioned simultaneous reconstruction algorithm (MLACF method or MLAA method) is used, subject mask projection data can be calculated utilizing the above-mentioned radioactivity image λ′ estimated by the simultaneous reconstruction algorithm. Further, the subject mask projection data may be calculated utilizing a radioactivity image estimated by a reconstruction algorithm (for example, the ML-EM method) different from the above-mentioned simultaneous reconstruction algorithm (MLACF method or MLAA method).
The reconstruction processing performed in the above-described offset estimation step may be performed by any one of an analytical reconstruction method, a statistical reconstruction method, and an algebraic reconstruction method. For example, there is an FBP (Filtered Back Projection) method as the analytical reconstruction. As the statistical reconstruction, there is, for example, the ML-EM (Maximum Likelihood-Expectation Maximization) method described above. As the algebraic reconstruction, for example, there is the ART (Algebraic Reconstruction Technique) method.
At least one or more of regions Ω extracted in the above-described reference region extraction step is a region of a tissue in which the attenuation coefficient is regarded as known. Here, “a region of a tissue in which an attenuation coefficient is regarded as known” is, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by a brain tissue, a region that can be approximated by a bone, a region that can be approximated by a lung tissue, a region that can be approximated by a soft tissue, and the like. Of course, the region is not limited to these illustrated tissues, but may be any tissues in which an approximation value of an attenuation coefficient can be known. In the case of a brain tissue, it is regarded as a region that can be approximated by water, so the attenuation coefficient value of water of 0.0096/mm can be used.
Regarding the coefficient a in the above-mentioned coefficient calculation step, there are a method of calculating based on a representative value as described below (the former method) and a method of calculating based on an error evaluation function as described below (the latter method).
In the former method, K (≥1) is a number of regions that can be approximated by a known attenuation coefficient value, Ωn is an nth region Ω, μnknown (n=1, . . . , K) is the known attenuation coefficient value of the region Ωn, S(X; Ωn) is a statistic of an image X in the region Ωn or a value calculated from the statistic as a representative value, T(x1, x2, . . . , xK) is any statistic of K values x1, x2, . . . . , xK or a value calculated from statistics of K values x1, x2, . . . , xK as a representative value, and αn is the coefficient α in the region Ωn. Here, the representative value is represented by, for example, a mean value, a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values. Of course, it is not limited to these exemplified values, but may be “a statistic or a value calculated from the statistic”.
When the image X is replaced with the image μ′, S(μ′; Ωn) is a representative value of the image μ′ in the region Ωn, and when the image X is replaced with the offset image μoff′, S(μoff, Ωn) is a representative value of the offset image μoff′ in the region Ωn. The known attenuation coefficient value μnknown in the region Ωn is equal to the value obtained by adding αn×S(μoff; Ωn) obtained by multiplying the coefficient αn in the region Ωn by the representative value S(μoff; Ωn) of the offset image μoff′ in the region Ωn to the representative value S(μ′; Ωn) of the image in the region Ωn. That is, the following formula is established: μnknown=S(μ′; Ωn)+αn×S(μoff; Ωn). Therefore, the coefficient αn in the region Ωn is calculated by αn=(μnknown−K(μ′; Ωn))/S(μoff; Ωn). By replacing K pieces of values x1, x2, . . . , xK with α1, α2, . . . , αK, respectively, T(α1, α2, . . . , αK) is a representative value of the coefficient α1, α2, . . . , αK. In summary, after calculating the coefficients α1, . . . , αK at each region Ω1, . . . , ΩK (with n=1, . . . , K, respectively, by setting the representative values T(α1, α2, . . . , αK) of the coefficients α1, . . . , αK as the coefficient α, the coefficient α can be calculated.
In the latter method, K(≥1) is a number of regions that can be approximated by a known attenuation coefficient value, Ωn is a nth region Ω, μnknown (n=1, . . . , K) is an image in which a known attenuation coefficient is set in the region Ωn, DΩn(X, Y) is an error evaluation function of an image X and an image Y within the region Ωn, and wn (n=1, . . . , K) is a coefficient range from 0 to 1. By replacing the image X with the image μnknown in which a known attenuation coefficient is set in the region Ωn and by replacing the image Y with the value (μ′+α×μoff) obtained by adding α×μoff obtained by multiplying the coefficient α by the offset image μoff′ to the image μ′, DΩn(μnknown, μ′×μoff) becomes an error evaluation function of the image μnknown in which a known attenuation coefficient is set in the region Ωn and an image (μ′+α×μoff) obtained by adding a non-uniform offset value to the quantitative attenuation coefficient image. By calculating a that minimizes the function f(α)(=Σn=1, . . . , K[Wn×DΩn(μnknown, μ′+α×μoff)]) with a coefficient α as a variable obtained by the weighted sum of DΩl(μlknown, μ′+α×μoff), . . . , DΩK(μKknown, μ′+α×μoff) by the coefficients w1, . . . , wK for each region Ω1, . . . , ΩK at n=1, . . . , K, the coefficient α can be calculated.
Furthermore, the attenuation coefficient image estimation program according to the present invention makes a computer execute the attenuation coefficient image estimation method according to the present invention.
According to the attenuation coefficient image estimation program according to the invention, by making a computer execute the attenuation coefficient image estimation method according to the present invention, the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α. Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
Furthermore, the positron CT apparatus according to the present invention is provided with a computing means for executing the attenuation coefficient image estimation program in the positron CT apparatus equipped with the attenuation coefficient image estimation program according to the present invention.
According to the positron CT apparatus of the present invention, the computing means configured to execute the attenuation coefficient image estimation program is provided, and the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α. Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
According to the attenuation coefficient image estimation method, the attenuation coefficient image estimation program, and the positron CT apparatus equipped with the same, the attenuation coefficient value is corrected in the attenuation coefficient value correction step based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α. Therefore, in the attenuation coefficient image having the attenuation coefficient value corrected in the attenuation coefficient value correction step, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
Hereinafter, Example 1 of the present invention will be described with reference to the drawings.
As shown in
Other than the above, the PET apparatus 1 is provided with a coincidence counting circuit 4 and an arithmetic circuit 5. Although only two connections from the γ-ray detectors 3 to the coincidence counting circuit 4 are shown in
The scintillator block 31 (see
Specifically, when radioactive pharmaceutical is administered to a subject (not illustrated), two γ-rays are generated due to the annihilation of the positron emitted from positron emission type RI. The coincidence counting circuit 4 checks the position of the scintillator block 31 (see
The detection signal data (count value) composed of appropriate data determined to be coincidence counting by the coincidence counting circuit 4 are sent to the arithmetic circuit 5. The arithmetic circuit 5 performs Steps S1 to S8 (see
Note that the attenuation coefficient image estimation program 6 is stored in a storage medium (not illustrated) represented by a ROM (Read-only Memory), etc. The attenuation coefficient image estimation program 6 is read from the storage medium to the arithmetic circuit 5, and the attenuation coefficient image estimation program 6 is executed by the arithmetic circuit 5, thereby performing the processing of the attenuation coefficient image estimation method shown in the flowchart of
As shown in
Further, as shown in
Here, the DOI detector is configured by laminating scintillator elements in the depth direction of radiation, and obtains the coordinate information in the depth direction (DOI: Depth of Interaction) and the lateral direction (direction in parallel to the incident surface) that caused the interaction by gravity center calculations. The spatial resolution in the depth direction can be further improved by using the DOI detector. Therefore, the number of layers of the DOI detector is the number of layers of scintillator elements stacked along the depth direction.
Next, specific functions of the arithmetic circuit 5 will be described with reference to
First, a subject is scanned by PET apparatus 1 shown in
A standard energy window (e.g., 400 keV to 600 keV), that is, a reconstruction data energy window, and the measurement range and the bin width of the TOF measurement data in the TOF direction are set. Here, note that the bin means discretizing (dividing). In the case of an image, a pixel corresponds to a bin. The TOF bin means a time division of the TOF information. For example, when the TOF bin is 100 [ps], the detection time difference is temporally separated with accuracy of 100 [ps].
From the list mode data, the TOF-PET measurement data is generated according to the settings.
Let μ′ be an image in which an non-uniform offset value is added to the quantitative attenuation coefficient image, and let λ′ be a non-quantitative radioactivity image. Based on the optimization of the evaluation function regarding the measurement data, the image μ′ and the radioactivity image λ′ are calculated simultaneously. As described in the “Means for Solving the Problems” section, the image μ′ also becomes an attenuation coefficient image, but is simply referred to as an “image ” in distinction from the quantitative attenuation coefficient image to be finally obtained.
The reconstruction algorithm in Step S1 is the simultaneous reconstruction algorithm in non-Patent Document 1. In Example 1, also in Examples 2 and 3 described later, the MLACF method described in non-Patent Document 1 is applied as the simultaneous reconstruction algorithm. In regard to the specific method of the MLACF method, please refer to non-Patent Document 1 mentioned above.
Let A′ be an attenuation coefficient sinogram. The radioactivity image λ′ and the attenuation coefficient sinogram A′ are estimated by the MLACF method. The attenuation coefficient sinogram A′ corresponds to the attenuation coefficient projection data in the present invention.
The attenuation coefficient sinogram A′ is reconstructed with a reconstruction algorithm (e.g., ML-TR method or ML-EM method) to generate a non-quantitative image μ′. In the case of using the ML-EM method, the attenuation coefficient sinogram A′ is log-transformed in advance. In regard to the specific method of the ML-TR method, please refer to Reference Document 1 (Reference Document 1: Erdoğan H, Fessler J A: Ordered subsets algorithms for transmission tomography. Phys Med Biol 44: 2835-2851, 1999). In regard to the specific method of the ML-EM method, please refer to Reference Document 2. (Reference 2: L. A. Shepp and Y. Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging, Vol. 1, pp. 113-122, 1982). Steps S1 and S2 correspond to the reconstruction calculation step in the present invention.
The image is binarization-processed by threshold processing. Then, a binarized image in which the subject region is “1” and the other regions are “0” is calculated as a subject mask image. Let mimg be a subject mask image.
The line integral data (projection data) of the subject mask image mimg is calculated (Projection). Then, by subjecting the projection data of the subject mask image mimg to binarization processing by threshold processing, binarized data in which the projection line passing through the subject is “1” and the other projection lines are “0” is calculated as subject mask projection data. Let mproj be the subject mask projection data. Steps S3 and S4 correspond to the mask calculation step in the present invention.
Let μoff be a non-uniform offset image. The offset image μoff is estimated by the reconstruction algorithm configured such that the forward projection data of the offset image μoff is approximated to the subject mask projection data mproj. That is, the subject mask projection data mproj is converted into image data by the reconstruction algorithm (for example, the ML-EM method). This image data is referred to as the offset image μoff. Step S5 corresponds to the offset estimation step in the present invention.
Let Ω be a region that can be approximated by a known attenuation coefficient value. At least one or more regions Ω are extracted using the image in which the subject region can be recognized calculated based on the measurement data (Extraction). In Example 1, also in Examples 2 to 4 described later, when K(≥1) is the number of regions that can be approximated by a known attenuation coefficient value and Ωn is the nth region Ω, respective regions Ω1, . . . , ΩK are extracted with n=1, . . . , K. For example, in the case of scanning a head of a subject, respective regions Ω1, . . . , ΩK are extracted at a region that can be approximated by air, a region that can be approximated by a brain tissue, and a region that can be approximated by a bone.
As an image that can be recognized by the subject region calculated based on the measurement data, for example, an image μ′ generated in Step S2, a radioactivity image λ′ obtained in Step S1, a non-quantitative image estimated by the reconstruction algorithm (e.g., ML-EM method) different from the reconstruction algorithm (simultaneous reconstruction algorithm) in Step S1, and a subject mask image mimg estimated from the above-mentioned subject mask projection data mproj can be exemplified. Step S6 corresponds to the reference region extraction step in the present invention.
Let μnknown (n=1, . . . , K) be a known attenuation coefficient value of the region Ωn, let S(X; Ωn) be a statistic of the image X in the region Ωn or a value calculated from the statistics as a representative value, let T(x1, x2, . . . , xK) be any statistic of K values x1, x2, . . . , xK or a value calculated from statistics of K values x1, x2, . . . , xK as a representative value , and let αn be the coefficient α in the region Ωn. Note that α is a coefficient. Here, the representative value is represented by, for example, a mean value, a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values. Here, the “trimmed mean value” means a mean value of the remaining data from which extremely large/small values are removed. Here, the “trimmed median value” means a median value of the remaining data from which extremely large/small values are removed.
When the image X is replaced with the image μ′, S(μ′; Ωn) is a representative value of the image μ′ in the region Ωn, and when the image X is replaced with the offset image μoff′, S(μoff′; Ωn) is a representative value of the offset image μoff in the region Ωn. The coefficient αn in the region Ωn is expressed by the following formula (1).
αn=(μnknown−S(μ′; Ωn))/S(μoff; Ωn) (1)
When K pieces of values x1, x2, . . . , xK are replaced with α1, α2, . . . , αK, respectively, T(α1, α2, . . . , αK) is a representative value of the coefficient α1, α2, . . . , αK. Therefore, the coefficient α is expressed by the following formula (2). Step S7 corresponds to the coefficient calculation step in the present invention.
α=T(α1, α2, . . . , αK) (2)
Let μ be the value (attenuation coefficient value) of an unknown true attenuation coefficient image. The attenuation coefficient value μ is expressed by the following formula (3).
μ=μ′+α×μoff (3)
Like the above formula (3), a value obtained by adding α×μoff obtained by multiplying the offset image μoff by the coefficient a to the value of the image μ′ is corrected as an attenuation coefficient value μ. Step S8 corresponds to the attenuation coefficient value correction step in the present invention.
The attenuation correction is performed using the attenuation coefficient image having the attenuation coefficient value μ obtained in Step S8. As described in the “Background Art” section, the transmittance of γ-rays from the estimated attenuation coefficient image is obtained, and the transmittance is divided from the PET measurement data by converting it into the data from which the influence of the γ-ray attenuation has been eliminated to perform the attenuation correction. Alternatively, the estimated attenuation coefficient image is incorporated into the calculation formula of the image reconstruction to obtain a reconstructed image from which the influence of the attenuation of γ-rays has been eliminated to perform the attenuation correction.
According to the attenuation coefficient image estimation method of this Example 1, in Steps S1 and S2, based on the optimization of the evaluation function regarding the measurement data (measurement data of TOF-PET) of the positron CT in which the time-of-flight information of the annihilation radiation is included, an image μ′ in which the non-uniform offset value is added to the quantitative attenuation coefficient image is calculated. At the same time, in Step S1, the radioactivity image λ′ is calculated. The reconstruction algorithm in Step S1 is the above-mentioned simultaneous reconstruction algorithm.
On the other hand, in Steps S3 and S4, the subject mask data (that is, subject mask projection data mproj) in the projection data space is calculated based on measurement data. In Step S5, the offset image μoff is estimated by the reconstruction algorithm configured such that the forward projection data of the offset image μoff is approximated to the subject mask projection data.
On the other hand, in Step S6, at least one or more regions Ω are extracted using the image in which the subject region can be recognized calculated based on the measurement data.
Here, as described in the “Means for Solving the Problems” section, the “image in which the subject region can be recognized calculated based on the measurement data” are, for example, an image μ generated in Step S2, a radioactivity image λ′ obtained in Step S1, a non-quantitative image estimated by the reconstruction algorithm (e.g., ML-EM method) different from the reconstruction algorithm (simultaneous reconstruction algorithm) in Step S1, and a subject mask image mimg estimated from the above-mentioned subject mask projection data mproj. Of course, the image is not limited to the illustrated images, and may be any image in which the subject region can be recognized calculated based on the measurement data. Further, as described in the “Means for Solving the Problems” section, “extracting at least one or more regions Ω using an image in which a subject region is recognizable calculated based on the measurement data” includes not only extracting the region Ω using a single piece of image information, but also extracting the region Ω using a combination of a plurality of pieces of image information (for example, logical sum or logical product).
Steps S7 and S8 are performed using the images obtained in the above-described Steps S1 to S6, the offset image μoff, and the region Q. In Step S7, the coefficient α which reduces the error between the value of the image μ′ in the region Ω and the known attenuation coefficient value is calculated. And, in Step S8, like the above-described formula (3), a value obtained by adding α×μoff obtained by multiplying the offset image μoff by the coefficient a to the value of the image μ′ is corrected as an attenuation coefficient value μ. In this way, the attenuation coefficient value is corrected in Step S8 based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α (i.e., μ≐μ′α×μoff). Therefore, in the attenuation coefficient image having the attenuation coefficient value μ corrected in Step S8, a systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
In Example 1, also in Examples 2 and 3 described later, Steps S1 and S2 corresponding to the above-mentioned reconstruction calculation step are performed by (b) a combination of a calculation algorithm in which an attenuation coefficient projection data is included as an unknown variable and an algorithm in which an image obtained by reconstructing the attenuation coefficient projection data is set as an image μ′.
The algorithm (b) is a combination of the MLACF method described in non-Patent Document 1 which simultaneously estimates the non-quantitative radioactivity image λ′ and the non-quantitative attenuation coefficient projection data (attenuation coefficient sinogram A′ in each Example 1 to 3) and an algorithm in which the image obtained by reconstructing the attenuation coefficient projection data (attenuation coefficient sinogram A′) is set as the image W. As described in the “Means for Solving the Problems” section, the algorithm in which the image obtained by reconstructing the attenuation coefficient projection data (attenuation coefficient sinogram A′) is set as the imageμ′ in the above-described (b) is not specifically limited, and may be any algorithm as long as it is a reconstruction algorithm. In
In Example 1, Steps S3 and S4 corresponding to the above-mentioned mask calculation step are performed. That is, the mask calculation step is composed of a step of calculating a binarized image of the image μ′ as a subject mask image mimg (Step S3), a step of calculating projection data of a subject mask image mimg (“projection” in the first half of Step S4), a step of calculating binarized data of the projection data of the subject mask image mimg as subject mask projection data mproj (“Binarization Processing” in the second half of Step S4). The image μ′ is an attenuation coefficient image that is not quantitative, but, as in Examples 2 and 3 described later, even if images other than the attenuation coefficient image (for example, radioactivity image λ′ or the radioactivity image μ2′ in Example 3) and projection data are binarized, the subject mask projection data mproj can be calculated.
The reconstruction processing performed in Step S5 corresponding to the above-mentioned offset estimation step is performed by the statistical reconstruction calculation method represented by the ML-EM (Maximum Likelihood—Expectation Maximization) method or the like in this Example 1. Of course, the reconstruction processing performed in Step S5 is not limited to the statistical reconstruction as in this Example 1. It may be performed by any calculation method of an analytical reconstruction, a statistical reconstruction, and an algebraic reconstruction. For example, there is an FBP (Filtered Back Projection) method as the analytical reconstruction. As the algebraic reconstruction, for example, there is an ART (Algebraic Reconstruction Technique) method.
At least one or more of regions Ω extracted in Step S6 corresponding to the above-described reference region extraction step is a region of a tissue in which the attenuation coefficient is regarded as known. Here, as described in the “Means for Solving the Problems” section, the “region of a tissue in which the attenuation coefficient is regarded as known” is, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by a brain tissue, a region that can be approximated by a bone, a region that can be approximated by a lung tissue, a region that can be approximated by a soft tissue, etc. Of course, the region is not limited to these exemplified tissues, but may be any tissues in which the approximation value of the attenuation coefficient can be known. In the case of a brain tissue, it is regarded as a region that can be approximated by water, so the attenuation coefficient value of water of 0.0096/mm can be used.
In this Example 1, Step S7 corresponding to the above-mentioned coefficient calculation step is performed. That is, In Example 1, also in the Examples 2 to 4 described above, the coefficient a is calculated based on the representative value. As described above, the representative value is represented by, for example, a mean value, a median value, a trimmed mean value, a trimmed median value, or a weighted mean value of two or more of these values. As described in the “Means for Solving the Problems” section, it is not limited to these exemplified values, but may be “a statistic or a value calculated from the statistic”.
When the image X is replaced with the image μ′, S(μ′; Ωn) is a representative value of the image in the region Ωn, and when the image X is replaced with the offset image μoff, S(μoff; Ωn) is a representative value of the offset image μoff′ in the region Ωn. A known attenuation coefficient value μnknown in the region Ωn is equal to the value obtained by adding αn×S(μoff; Ωn) ) obtained by multiplying the coefficient αn in the region Ωn by the representative value S(μoff; Ωn) of the offset image μoff′ in the region Ωn to the representative value S(μ′; Ωn) of the image μ′ in the region Ωn. That is, the following formula is established: μnknown=S(μ′; Ωn)+αn×S(μoff; Ωn). Therefore, as in the above-described formula (1), the coefficient αn in the region Ωn is calculated by αn=(μnknown−S(μ′; Ωn))/S(μoff; Ωn). When K pieces of values x1, x2, . . . , xK are replaced with α1, α2, . . . , αK, respectively, T(α1, α2, . . . , αK) is a representative value of the coefficient α1, α2, . . . , αK. In summary, after calculating the coefficients α1, . . . , αK at each region Ω1, . . . , ΩK with n=1, . . . , K, respectively, as in the above-described formula (2), by setting the representative values T(α1, α2, . . . , αK) of the coefficients α1, . . . , αK as the coefficient α the coefficient α can be calculated.
According to the attenuation coefficient image estimation program 6 (see
According to the PET apparatus 1 (see
Next, Example 2 of the present invention will be described with reference to the attached drawings.
In Example 1 described above, the binarized image of the image μ′ is calculated as a subject mask image mimg, the projection data of the subject mask image mimg is calculated, and the binarized data of the projection data of the subject mask image mimg is calculated as subject mask projection data mproj. On the other hand, in this Example 2, the binarized data obtained by converting the measurement data of TOF-PET into a projection data format is calculated as subject mask projection data mproj.
Step S11 of
Step S12 of
In Example 1 described above, Steps S3 and S4 of
Step S15 of
Step S16 of
Step S17 of
Step S18 of
According to the attenuation coefficient image estimation method of this Example 2, in the same manner as in the above-described Example 1, the attenuation coefficient value is corrected in Step S18 based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α. Therefore, in the attenuation coefficient image having the attenuation coefficient value μ corrected in Step S18, the systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
In this Example 2, Step S14 corresponding to the above-mentioned coefficient calculation step is performed. That is, the mask calculation step includes the step of calculating binarized data obtained by converting the measurement data of TOF-PET described above into the projection data format as subject mask projection data (Step S14). In the case of this Example 2, the binarized data obtained by directly converting the measurement data of TOF-PET into a projection data format can be calculated as mask projection data mproj.
The functions and effects of the attenuation coefficient image estimation program 6 (see
Next, Example 3 of the present invention will be described with reference to the attached drawings.
In Example 1 described above, the binarized image of the image μ′ is calculated as a subject mask image mimg, the projection data of the subject mask image mimg is calculated, and the binarized data of the projection data of the subject mask image mimg is calculated as subject mask projection data mproj. Further, in the above-described Example 2, the binarized data obtained by converting the measurement data of TOF-PET into a projection data format is calculated as subject mask projection data mproj. On the other hand, in this Example 3, based on the optimization of evaluation function for measurement data of TOF-PET, the radioactivity image is calculated, the projection data of the radioactivity image is calculated, the binarized data of projection data (of radioactivity image) is calculated as subject mask projection data mproj.
First, the case of calculating the subject mask projection data mproj utilizing a radioactivity image estimated by the MLACF method will be described with reference to
Step S21 of
Step S22 of
In Example 1 described above, Steps S3 and S4 of
First, in
Step S25 of
Step S26 of
Step S27 of
Step S28 of
Next, the case of calculating the subject mask projection data mproj utilizing the radioactivity image estimated by the reconstruction algorithm different from the MLACF method will be described with reference to
Step S31 of
Step S32 of
In
First, in
The line integral data (projection data) of the radioactivity image λ2′ estimated based on the optimization of the evaluation function regarding the measurement data in the reconstruction algorithm different from the MLACF method is calculated (Projection). Then, by subjecting the projection data of the radioactivity image λ2′ to binarization processing by the threshold processing, binarized data in which the projection line passing through the subject is “1” and the other projection lines are “0” is calculated as subject mask projection data mproj. Steps S33 and S34 correspond to the mask calculation step in the present invention.
Step S35 of
Step S36 of
Step S37 of
Step S38 of
In the attenuation coefficient image estimation method of this Example 3, in the same manner as in the above-described Examples 1 and 2, the attenuation coefficient value is corrected in Step S28 of
In this Example 3, Step S24 of
The functions and effects of the attenuation coefficient image estimation program 6 (see
Next, Example 4 of the present invention will be described with reference to the attached drawings.
In Examples 1 to 3 as described above, the above-mentioned reconstruction calculation step is performed by the combination of the MLACF method and an algorithm in which the image obtained by reconstructing the attenuation coefficient projection data (in each of Examples 1 to 3, attenuation coefficient sinogram A′) is set as the image μ′. On the other hand, in this Example 4, (a) it is performed by a calculation algorithm (MLAA method) in which the image μ′ is included as an unknown variable.
In Examples 1 to 3 described above, in order to calculate the image μ and the radioactivity image λ′ simultaneously, after Step S1 (Step S11 in Example 2 and Step S21 or S31 in Example 3) in which the radioactivity image λ′ and the attenuation coefficient sinogram A′ are estimated by the MLACF method, Step S2 (Step S12 in Example 2, Steps S22 or S32 in Example 3) in which an image obtained by reconstructing the attenuation coefficient sinogram A′ is set to the image is performed. In this Example 4, the radioactivity image λ′ and the image are simultaneously calculated by the MLAA method.
That is, two Steps S1 and S2 (Steps S1 and S12 in Example 2, Steps S21 and S22 or S31 and S32 in Example 3) using the MLACF method are integrated into one Step S41 when the MLAA method is used in this Example 4. As for the specific method of the ML-EM method, please refer to Reference Document 3 (Reference Document 3: A Rezaei (K. U. Leuven), M. Defrise, G. Bal et. al., “Simultaneous reconstruction of activity and attenuation in time-of-flight PET”, IEEE Trans. Med. Imag., 31 (12), 2224-2233, 2012). Steps S41 corresponds to the reconstruction calculation step in the present invention.
Step S43 of
Step S44 of
Step S45 of
Step S46 of
Step S47 of
Step S48 of
According to the attenuation coefficient image estimation method of this Example 4, in the same manner as in the above-described Examples 1 to 3, the attenuation coefficient value is corrected in Step S48 based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α. Therefore, in the attenuation coefficient image having the attenuation coefficient value μ corrected in Step S48, a systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
In this Example 4, Step S41 corresponding to the above-mentioned reconstruction calculation step may be performed by (a) a calculation algorithm in which the image μ′ is included as an unknown variable. The algorithm (a) is an MLAA method that simultaneously reconstructs the non-quantitative radioactivity image λ′ and the image μ (non-quantitative attenuation coefficient image).
The functions and effects of the attenuation coefficient image estimation program 6 (see
Next, Example 5 of the present invention will be described with reference to the attached drawings.
In the above-described Examples 1 to 4, the coefficient a is calculated based on the representative value. On the other hand, in this Example 5, the coefficient a is calculated based on the error evaluation function.
Step S51 of
Step S52 of
Step S53 of
Step S54 of
Step S55 of
Step S56 of
In the above-described Examples 1 to 4, the coefficient α is calculated based on the representative value. In this Example 5, the coefficient α is calculated based on the error evaluation function. When K(≥1) is the number of regions that can be approximated by a known attenuation coefficient value and wn (n=1, . . . , K) is a coefficient range from 0 to 1, in
Specifically, let μknown be an image in which a known attenuation coefficient is set in the known attenuation coefficient in the region Ω, and let DΩ (X, Y) be an error evaluation function of the image X and the image Y in the region Ω. When the image X is replaced with the image μknown in which a known attenuation coefficient is set in the known attenuation coefficient in the region Ω and the image Y is replaced with the value (μ′+α×μoff) obtained by adding α×μoff obtained by multiplying the offset image μoff′ by the coefficient α to the image μ′, DΩ (μknown, μ′+μoff) becomes the error evaluation function of the image μknown in which the known attenuation coefficient regarding the region Ω is set and the image (μ′+α×μoff) obtained by adding the non-uniform offset value to the quantitative attenuation coefficient image. When f(α) is a function having a coefficient α as a variable, the function f(α) is expressed by the following formula (4).
f(α)=DΩ(μknown, μ′+α×μoff) (4)
α that minimizes the function f(α) expressed by the formula (4) is calculated. The error evaluation function DΩ(X, Y) is, for example, a quadratic function DΩ(X, Y)=Σn∈Ω(X−Y)2. Of course, when it is a function that evaluates the error of the image X and the image Y, the error evaluation function DΩ(X, Y) as exemplified in the difference sum DΩ(X, Y)=Σn∈Ω|X−Y| of the absolute value is not particularly limited. Step S57 corresponds to the coefficient calculation step in the present invention.
Step S48 of
According to the attenuation coefficient image estimation method of this Example 5, in the same manner as in the above-described Examples 1 to 4, the attenuation coefficient value is corrected in Step S58 based on the mathematical relationship in which the difference between the value of the non-quantitative image μ′ in the region Ω and the known attenuation coefficient value (the value of the true attenuation coefficient image) can be approximated by α×μoff obtained by multiplying the offset image μoff by the coefficient α. Therefore, in the attenuation coefficient image having the attenuation coefficient value μ corrected in Step S58, a systematic error becomes small. As a result, a quantitative attenuation coefficient image can be generated, which enables an accurate attenuation correction of the radioactivity image.
In this Example 5, the coefficient α is calculated based on the error evaluation function. The case in which the above formula (4) is generalized will be described. Let K(≥1) be a region that can be approximated by a known attenuation coefficient value, let Ωn be the nth region Ω, let μnknown(n=1, . . . , K) be an image in which a known attenuation coefficient is set in the region Ωn, let DΩn(X, Y) be an error evaluation function of an image X and an image Y within the region Ωn, and let wn (n=1, . . . , K) be a coefficient range from 0 to 1. When the image X is replaced with the image μnknown in which a known attenuation coefficient is set in the known attenuation coefficient in the region Ω and the image Y is replaced with the value (μ′+α×μoff) obtained by adding α×μoff obtained by multiplying the offset image μoff′ by the coefficient a to the image μ′, DΩn (μthknown, μ′+α×μoff) becomes the error evaluation function of the image μnknown in which the known attenuation coefficient regarding the region Ωn is set and the image (μ′+α=μoff) obtained by adding the non-uniform offset value to the quantitative attenuation coefficient image. At this time, the function f(α) in which the coefficient α is represented by weighted sum of DΩ1(μ1known, μ′+α×μoff), . . . , DΩK ((μKknown, μ′+α×μoff) by the coefficient w1, . . . , wK for each region Ω1, . . . , ΩK, n=1, . . . , K. That is, when generalized, the function f(α) is expressed by the following formula (5).
f(α)=Σn=1, . . , K[wn×DΩn(μnknown, μ′+α×μoff)] (5)
α that minimizes the function f(α) expressed by the formula (5) is calculated.
The functions and effects of the attenuation coefficient image estimation program 6 (see
The present invention is not limited to the above-described embodiment, and can be modified as follows.
(1) in each of the above-described Examples, the subject to be imaged is not particularly limited. The present invention may be applied to an apparatus for imaging an entire body of a subject, an apparatus for imaging a head of a subject, and an apparatus for imaging a breast of a subject.
(2) In each of the above-described Examples, although the DOI detector is used, the present invention may be applied to a detector that does not discriminate the depth direction.
(3) in each of the above-described Example, the detector ring is stacked along the axial direction of the subject. However, the detector ring may have only one detector ring.
(4) in each of the embodiments described above, the data format is a sinogram but the present invention is not limited to a sinogram. As long as it is projection data, for example, the data format may be a histogram. Therefore, in Examples 1 to 3 described above, the attenuation coefficient projection data estimated by the MLACF method is the attenuation coefficient sinogram A′, but the attenuation coefficient projection data estimated by the MLACF method may be the attenuation coefficient histogram.
(5) In Example 1 described above, the projection data is calculated after binarizing the image μ′ first, the and projection data is binarized. However, the subject mask projection data mproj may be calculated as follows. That is, the mask calculation step may be an aspect including a step of calculating projection data of the image μ′ and a step of calculating binarized data of the projection data of the imageμ′ as a subject mask projection data mproj. In the case of this aspect, the projection data of the image μ′ is first calculated and then binarized.
(6) In Example 3 described above, the projection data of the radioactivity image (λ′ in
As described above, the present invention is suitable for estimation of an attenuation coefficient image using measurement data measured by a TOF measurement type PET apparatus.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2017/019944 | 5/29/2017 | WO | 00 |
