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Spiral imaging is a popular fast MRI (Magnetic Resonance Imaging) data acquisition strategy. Flow artifacts are usually not apparent in images reconstructed using spiral techniques due to inherently nulled gradient moments of the spiral trajectories. However, off-resonance effects may lead to blurring artifacts in spiral imaging. Additionally, specific blurring artifacts due to fat spins may be difficult to correct using conventional spiral off-resonance correction methods.
Spiral Dixon techniques using conventional spatially selective RF (radio frequency) pulses may be based on conventional Dixon techniques in rectilinear acquisitions. These spiral Dixon techniques may achieve unambiguous water-fat signal separation with effective blurring artifact correction, even in the presence of B0 inhomogeneity. In Spiral three-point Dixon (S3PD) techniques, a frequency field map can be generated using methods analogous to rectilinear three point Dixon (3PD) techniques since off-resonance blurred signals do not affect the phase difference between the first and third data sets. De-blurred images may then be reconstructed using the frequency field map. However, three point spiral techniques may be computationally intensive. Thus two point techniques may be employed.
Spiral two-point Dixon (S2PD) techniques may be employed to facilitate unambiguous water-fat decomposition in spiral imaging with fewer computations than S3PD techniques. S2PD techniques may also facilitate correcting for off-resonance blurring artifacts using only two data sets. S2PD techniques may acquire the two data sets with different TEs (echo times). However, direct computation of a frequency field map in S2PD techniques may be complicated by the phase relationship between water and fat spins being disrupted by off-resonance blurred signals. Thus, to achieve both water-fat decomposition and signal de-blurring, off-resonance correction at multiple predetermined frequencies may be required in these conventional techniques. For example, in an S2PD technique that employs multi-frequency testing, several predetermined off-resonance frequencies may be tested to facilitate separating water and fat signals and de-blurring the decomposed images. However, the range of tested frequencies must be large enough to span a full range of anticipated B0 variations, and thus S2PD techniques may also be computationally intensive.
Block regional off-resonance correction (BRORC) techniques may also be employed to facilitate correcting for off-resonance blurring artifacts in conventional spiral acquisitions. BRORC has been used with spiral acquisitions using spatial-spectral RF pulses (SPSP pulses). In BRORC, off-resonance correction proceeds block-by-block through a reconstructed image under the assumption that each small sub-image block has a constant B0 off-resonance frequency. This assumption is valid in most cases since magnetic field inhomogeneities are usually smoothly varying across a field-of-view (FOV). BRORC is typically several times more computationally efficient than the conventional frequency-segmented off-resonance correction with no perceptual difference between the images.
The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate various example systems, methods, and so on, that illustrate various example embodiments of aspects of the invention. It will be appreciated that the illustrated element boundaries (e.g., boxes, groups of boxes, or other shapes) in the figures represent one example of the boundaries. One of ordinary skill in the art will appreciate that one element may be designed as multiple elements or that multiple elements may be designed as one element. An element shown as an internal component of another element may be implemented as an external component and vice versa. Furthermore, elements may not be drawn to scale.
and φ in a BRORC-S2PD technique.
Example systems and methods described herein employ a BRORC-S2PD (block regional off-resonance correction, spiral two point Dixon) technique to estimate local B0 off-resonance frequencies in a B0 field produced by an MRI apparatus and to produce a map of those estimated B0 off resonance frequencies. The estimated B0 off-resonance frequency field map may then facilitate performing both water-fat decomposition and blurring artifact correction in a block-by-block manner. The example block-by-block approaches produce improvements in computational efficiency over conventional S2PD algorithms.
In BRORC-S2PD techniques, a local B0 inhomogeneity in a B0 field present when an MRI image is acquired is estimated on a block-by-block basis in the image domain. This block-by-block approach eliminates the need for multi-frequency testing and thus reduces computational complexity and intensity. In one example, both frequency estimation and off-resonance artifact correction proceed block-by-block through a reconstructed image.
The following includes definitions of selected terms employed herein. The definitions include various examples and/or forms of components that fall within the scope of a term and that may be used for implementation. The examples are not intended to be limiting. Both singular and plural forms of terms may be within the definitions.
“Computer-readable medium”, as used herein, refers to a medium that participates in directly or indirectly providing signals, instructions and/or data. A computer-readable medium may take forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media may include, for example, optical or magnetic disks, and so on. Volatile media may include, for example, optical or magnetic disks, dynamic memory and the like. Transmission media may include coaxial cables, copper wire, fiber optic cables, and the like. Transmission media can also take the form of electromagnetic radiation, like that generated during radio-wave and infra-red data communications, or take the form of one or more groups of signals. Common forms of a computer-readable medium include, but are not limited to, a floppy disk, a flexible disk, a hard disk, a magnetic tape, other magnetic media, a CD-ROM, other optical media, punch cards, paper tape, other physical media with patterns of holes, a RAM, a ROM, an EPROM, a FLASH-EPROM, or other memory chip or card, a memory stick, a carrier wave/pulse, and other media from which a computer, a processor or other electronic device can read. Signals used to propagate instructions or other software over a network, like the Internet, can be considered a “computer-readable medium.”
“Data store”, as used herein, refers to a physical and/or logical entity that can store data. A data store may be, for example, a database, a table, a file, a list, a queue, a heap, a memory, a register, and so on. A data store may reside in one logical and/or physical entity and/or may be distributed between two or more logical and/or physical entities.
“Logic”, as used herein, includes but is not limited to hardware, firmware, software and/or combinations of each to perform a function(s) or an action(s), and/or to cause a function or action from another logic, method, and/or system. For example, based on a desired application or needs, logic may include a software controlled microprocessor, discrete logic like an application specific integrated circuit (ASIC), a programmed logic device, a memory device containing instructions, or the like. Logic may include one or more gates, combinations of gates, or other circuit components. Logic may also be fully embodied as software. Where multiple logical logics are described, it may be possible to incorporate the multiple logical logics into one physical logic. Similarly, where a single logical logic is described, it may be possible to distribute that single logical logic between multiple physical logics.
An “operable connection”, or a connection by which entities are “operably connected”, is one in which signals, physical communications, and/or logical communications may be sent and/or received. Typically, an operable connection includes a physical interface, an electrical interface, and/or a data interface, but it is to be noted that an operable connection may include differing combinations of these or other types of connections sufficient to allow operable control. For example, two entities can be operably connected by being able to communicate signals to each other directly or through one or more intermediate entities like a processor, operating system, a logic, software, or other entity. Logical and/or physical communication channels can be used to create an operable connection.
“Software”, as used herein, includes but is not limited to, one or more computer or processor instructions that can be read, interpreted, compiled, and/or executed and that cause a computer, processor, or other electronic device to perform functions, actions and/or behave in a desired manner. The instructions may be embodied in various forms like routines, algorithms, modules, methods, threads, and/or programs including separate applications or code from dynamically and/or statically linked libraries. Software may also be implemented in a variety of executable and/or loadable forms including, but not limited to, a stand-alone program, a function call (local and/or remote), a servelet, an applet, instructions stored in a memory, part of an operating system or other types of executable instructions. It will be appreciated by one of ordinary skill in the art that the form of software may depend, for example, on requirements of a desired application, the environment in which it runs, and/or the desires of a designer/programmer or the like. It will also be appreciated that computer-readable and/or executable instructions can be located in one logic and/or distributed between two or more communicating, co-operating, and/or parallel processing logics and thus can be loaded and/or executed in serial, parallel, massively parallel and other manners.
Suitable software for implementing the various components of the example systems and methods described herein may be produced using programming languages and tools like Java, Pascal, C#, C++, C, CGI, Perl, SQL, APIs, SDKs, assembly, firmware, microcode, and/or other languages and tools. Software, whether an entire system or a component of a system, may be embodied as an article of manufacture and maintained or provided as part of a computer-readable medium as defined previously. Another form of the software may include signals that transmit program code of the software to a recipient over a network or other communication medium. Thus, in one example, a computer-readable medium has a form of signals that represent the software/firmware as it is downloaded from a web server to a user. In another example, the computer-readable medium has a form of the software/firmware as it is maintained on the web server. Other forms may also be used.
“User”, as used herein, includes but is not limited to one or more persons, software, computers or other devices, or combinations of these.
Some portions of the detailed descriptions that follow are presented in terms of algorithms and symbolic representations of operations on data bits within a memory. These algorithmic descriptions and representations are the means used by those skilled in the art to convey the substance of their work to others. An algorithm is here, and generally, conceived to be a sequence of operations that produce a result. The operations may include physical manipulations of physical quantities. Usually, though not necessarily, the physical quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated in a logic and the like.
It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like. It should be borne in mind, however, that these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise, it is appreciated that throughout the description, terms like processing, computing, calculating, determining, displaying, or the like, refer to actions and processes of a computer system, logic, processor, or similar electronic device that manipulates and transforms data represented as physical (electronic) quantities.
In an S2PD technique, two reconstructed images (S0 and S1) may be acquired using normal spatially selective RF pulses in pulse sequence repetitions. The TEs (echo times) of S0 and S1 are set to nτ and (n+1)τ, respectively, where n is a positive integer and τ is the time during which fat spins precess 180° out of phase with respect to water spins. With this condition, the signals at each pixel in the reconstructed images (S0 and S1) can be expressed as:
S0=W′+F′ [Equation 1]
S1=(W′−F′)exp(iφ) [Equation 2]
where W′ is a water signal blurred by a local B0 inhomogeneity off-resonance frequency f (Hz), F′ is a fat signal blurred by the local B0 inhomogeneity and a chemical-shift off-resonance frequencies f+ffat (Hz), and φ is the phase shift due to the B0 inhomogeneity off-resonance effects during τ. That is,
φ=2πf·τ [Equation 3]
S0 and S1 will be used through the description and the claims in this application to refer to the two reconstructed images acquired using the above-described MRI acquisition parameters. One example BRORC-S2PD technique includes two steps. First, as illustrated in
B0 off-resonance frequency estimation may be performed efficiently using a block-based approach. If blurring artifacts are negligible in data sets acquired using an S2PD technique, then idealized signals in S0 and S1 may be defined as Ŝ0 and Ŝ1. In this case, Equations 1 and 2 may be rewritten as:
Ŝ0=W+F [Equation 4]
Ŝ1=(W−F)exp(iφ) [Equation 5]
where W and F are water and fat signals free of blurring artifacts. Now consider a function T(θ):
From this definition, T(θ) is a periodic function of θ with a period 2π. T(θ), when used in the description and claims in this application will refer to this periodic function of θ. When θ=φ, Equation 7 follows:
W and F may be aligned when n is even and may be opposed when n is odd. In either case, Equation 7 yields a real value.
and an angle φ. Suppose that
is a vector indicated by dashed arrow 100. Solid circle 110 represents all possible values that T(θ) can take. T(φ) is real. As indicated in
where Im( ) and Re( ) represent the imaginary and real parts of the quantities within the parentheses.
Equations 4 through 8 and the discussion associated therewith assume that the blurring artifacts of water and fat signals in Ŝ0 and Ŝ1 are negligible. However, in some examples, blurring artifacts cannot be ignored. A method to efficiently estimate a local B0 frequency from the original blurred signals for sub-image regions is described below. This method may be employed on a block-by-block basis to facilitate producing a map that records local B0 off-resonance frequency estimations.
Wg′=(S0+S1 exp(−iφg))/2 [Equation 9], and
Fg′=(S0−S1 exp(−iφg))/2 [Equation 10], with
φg=2πfg·τ [Equation 11]
where Wg′250 and Fg′ 260 are the decomposed water and fat M1×M1 sub-images. For subsequent sub-image matrices, the guess frequency may be based, at least in part, on an estimated frequency in a neighboring block(s).
Blurring artifacts in Wg′ 250 and Fg′ 260 may now be reduced by a frequency demodulation logic 270. To generate a de-blurred water image Wg 280 from Wg′ 250, the frequency demodulation logic 270 may perform a 2D-FFT (Fast Fourier Transform) on Wg′ 250 to obtain Fourier data. The frequency demodulation logic 270 may perform frequency demodulation on the Fourier data with the frequency fg. Although it is possible to demodulate an entire M1×M1 Fourier data, frequency demodulation may also be performed on lower-frequency components like a central m1×m1 Fourier data matrix (m1≦M1) to reduce computational costs. In one example, high resolution sub-images are not employed since the process flow illustrated in
A de-blurred fat sub-image Fg 282 can be reconstructed from Fg′ 260 using the same procedures as described above but with the demodulation frequency fg+ffat. Local frequency estimation may then be performed by a frequency estimation logic 284.
Central matrices Wgc 286 and Fgc 288 may be extracted from Wg 280 and Fg 282 to facilitate avoiding artifacts in the outer regions of Wg 280 and Fg 282. The central matrices may be, for example, 2 pixels by 2 pixels in size. Tgc may be computed by the frequency estimation logic 284 from Wgc 286 and Fgc 288 using:
In Equation 12, element-by-element division is performed within the parentheses, and the bar denotes the average of the elements of the matrix in the parentheses. If fg is close to the true B0 off-resonance frequency f, then the off-resonance blurring artifacts contained in Wgc 286 and Fgc 288 may be insignificant. Therefore Tgc in Equation 12 is approximately equal to T(φg):
Tgc≅=T(φg) [Equation 13]
Thus, the first actual estimate of the local B0 off-resonance frequency fe, may be determined by the frequency estimation logic 284 using:
fe=fg−fd [Equation 14], with
That is, fd is an estimate of the difference between the original guess frequency fg and the true local off-resonance frequency f. Thus, Equations 14 and 15 may be viewed as a re-evaluation of Equation 8 with a conversion from phase to frequency. Frequency estimation errors may then be reduced.
An initial estimated B0 off-resonance frequency field map 290 can be formed by the frequency estimation logic 284 by setting the computed off-resonance frequency fe in a location in the field map 290 associated with the sub-images S0 220 and S1 230 to the central r1M1×r1M1 pixels 292 of the M1×M1 matrix region 294. A final estimated B0 off-resonance frequency field map 298 may then be created by applying a low pass filter 296 to the initial estimated field map 290.
The value of fe given by Equations 14 and 15 may be relatively accurate if the region corresponding to Wgc 286 and/or Fgc 288 contains either predominantly water or fat tissue. However, frequency estimation may be unstable for voxels containing nearly equal water and fat signals. Therefore, a regularization function R may be introduced into Equation 14:
fe=fg−R·fd [Equation 16]
An example function R is illustrated in
As shown in
Block-based region growing actions may be performed to facilitate providing an estimated frequency for the guess frequency used in subsequent repetitions. By way of illustration, a B0 frequency associated with a first r1M1×r1M1 block may be determined using Equations 14 and 15. An initial guess frequency fg may be supplied, for example, by a user. In the example, the fg may be a pure guess (e.g., 0 Hz) in the first evaluation of Equations 14 and 15. Then, Equations 14 and 15 may be re-evaluated after the output fe is set to fg. This process may be repeated until fe becomes substantially constant. After the B0 frequency is estimated for the first r1M1×r1M1 block, local B0 frequencies of neighboring blocks may be estimated using Equation 16. The output fe of the frequency-determined block may then be used in subsequent calculations as the fg for frequency estimation of the neighboring blocks.
A low pass filter 296 (
As with the processing illustrated in
A water sub-image logic 540 may then separate water signals in the M2×M2 sub-image matrices to produce a separated sub-image W′ 550. A frequency demodulator 560 may then demodulate the separated sub-image W′ 550 to produce W 570. Both water signal separation and frequency demodulation may be performed for the extracted M2×M2 matrices based on the frequency {overscore (f)}e. The separation of water signals and frequency demodulation are performed assuming that the region associated with the M2×M2 matrices has a constant B0 off-resonance frequency {overscore (f)}e. In one example, {overscore (f)}e is the mean B0 off-resonance frequency of the central r2M2×r2M2 pixels (0<r2≦1) in the M2×M2 matrices in the estimated B0 off-resonance frequency field map. While the mean B0 off-resonance frequency is described, it is to be appreciated that {overscore (f)}e may be selected in other manners. In one example, the water sub-image may be computed using:
W′=(S0+S1 exp(−iφe))/2 [Equation 17], where
φe=2π{overscore (f)}e·τ [Equation 18].
The water sub-image W′ 550 may exhibit blurring artifacts. Therefore, de-blurring may be performed for sub-image W′ 550. As described above, frequency demodulator 560 may frequency demodulate W′ 550 to produce demodulated water-image data. Then, the de-blurred water sub-image W 570 is obtained when the frequency demodulator 560 performs a 2D-inverse Fourier transform on the demodulated water image data. Since the outer regions of W 570 may exhibit artifacts, in one example only the central r2M2×r2M2 pixels of W 570 are retained for insertion into a final reconstructed image. The flow illustrated in
A fat image can also be reconstructed using procedures similar to those in
F′=({tilde over (S)}0−{tilde over (S)}1 exp(−iφe))/2 [Equation 19]
As F′ may exhibit blurring artifacts due to the local B0 off-resonance frequency, F′ may be demodulated with the frequency {overscore (f)}e to reconstruct a de-blurred sub-image F. Like the de-blurred water sub-image W 570, in some examples only the central r2M2×r2M2 pixels of F are retained for insertion into a final reconstructed image.
In one example, both the block-based frequency estimation method and the block-based signal decomposition and de-blurring method can be applied to specific regions of interest in S0 and S1 rather than to an entire image. This is not possible using conventional S2PD techniques.
Computational costs of the BRORC-S2PD techniques and S2PD techniques may be compared to illustrate improved computational efficiency. In one example, the total number of complex multiplications required for water image reconstruction using an example BRORC-S2PD technique can be expressed as:
BS2PD(W)=(2·2N2 log2 N)+(s1·2(M12+2M12 log2 M1+m12+2m12 log2 m1))+(s2·(M22+2M22 log2 M2+M22+2M22 log2 M2)) [Equation 20]
where s1 and s2 are the total number of r1M1×r1M1 blocks and that of r2M2×r2M2 blocks, respectively, necessary to cover the scanned object regions. In Equation 20, the first, second, and third sections describe the number of complex multiplications required for the original image reconstruction (two N×N images with different TEs), those for frequency estimation, and those necessary for the water image reconstruction, respectively. The computational costs for other operations like those associated with Equations 12, 15, and 16 are ignored in Equation 20.
The total number of complex multiplications required for water image reconstruction in a conventional S2PD technique can be expressed as:
S2PD(W)=L·2(N2+N2+2N2 log2 N) [Equation 21]
In Equation 21, the first, second and third terms within the parentheses express the number of complex multiplications required for signal decomposition, frequency-demodulation, and 2D-FFT on N×N k-space data, respectively, with a particular tested B0 off-resonance frequency. The computational costs for other operations like those necessary for frequency determination, are ignored in Equation 21. The factor 2 before the parenthesis in Equation 21 results from the fact that water and fat images are simultaneously reconstructed in the S2PD technique.
Table 1 summarizes the total number of complex multiplications required for example image reconstructions. An example BRORC-S2PD technique was applied to the scanned object regions and not to the background in image 600 (
a s1 denotes the total number of blocks processed for frequency estimation in the BRORC-S2PD algorithm.
b s2 denotes the total number of blocks processed for water image reconstruction in the BRORC-S2PD algorithm.
c the total number of complex multiplications if the entire image matrix is processed.
Example methods may be better appreciated with reference to the flow diagrams of
In the flow diagrams, blocks denote “processing blocks” that may be implemented with logic. The processing blocks may represent a method step and/or an apparatus element for performing the method step. A flow diagram does not depict syntax for any particular programming language, methodology, or style (e.g., procedural, object-oriented). Rather, a flow diagram illustrates functional information one skilled in the art may employ to develop logic to perform the illustrated processing. It will be appreciated that in some examples, program elements like temporary variables, routine loops, and so on, are not shown. It will be further appreciated that electronic and software applications may involve dynamic and flexible processes so that the illustrated blocks can be performed in other sequences that are different from those shown and/or that blocks may be combined or separated into multiple components. It will be appreciated that the processes may be implemented using various programming approaches like machine language, procedural, object oriented and/or artificial intelligence techniques.
At 920, a field map may be created in a block-by-block manner using block-based local B0 off resonance frequency estimations. Creating the field map may include several actions. Thus,
Method 1000 may include, at 1010, extracting sub-image matrices from related locations in S0 and S1. At 1020, a guess frequency may be established for use in decomposing the extracted sub-image matrices. As described above, the guess frequency may be a pure guess, may be based on values for neighboring regions, and so on. At 1030, the extracted sub-image matrices may be processed to produce water-fat decomposed sub-images. In one example, the water-fat decomposed sub-images may be processed according to:
Wg′=(S0+S1 exp(−iφg))/2 [Equation 9], and
Fg′=(S0−S1 exp(−iφg))/2 [Equation 10], with
φg=2πfg·τ [Equation 11]
where Wg′ and Fg′ are the decomposed water and fat sub-images.
At 1040, blurring artifacts may be reduced in the decomposed water and fat sub-images. In one example, to generate a de-blurred water sub-image Wg from Wg′, a 2D-FFT is performed on Wg′ to obtain Fourier data. Frequency demodulation is then performed on the Fourier data with the frequency fg. A 2D-IFFT may then be performed on the demodulated Fourier data to reconstruct de-blurred water sub-image Wg. As described above, a de-blurred fat sub-image may be produced using a similar technique.
At 1050, central matrices Wgc and Fgc may be extracted from Wg and Fg. Signals in the central matrices Wgc and Fgc may then be used for frequency estimation as described by Equation 16. For example, at 1060, Tgc may be computed from Wgc and Fgc using:
At 1070, an element in an initial estimated B0 off-resonance frequency field map can be established by setting the computed off-resonance frequency to fe for a central region described by the r1M1×r1M1 pixels associated with the region from which the sub-image matrices were extracted at 1010. In one example fe may be determined using:
fe=fg−fd [Equation 14], with
At 1080, a determination may be made concerning whether to process another block. If the determination is Yes, then processing may return to 1010. Otherwise processing may proceed to 1090. At 1090, a final estimated B0 off-resonance frequency field map may be created by applying a low pass filter to the initial map constructed by repetitions of the actions 1010 through 1070.
While
At 1210, sub-image matrices may be extracted from corresponding locations in the images S0 and S1. At 1220, an estimated frequency may be retrieved from the estimated B0 off-resonance frequency field map created at 1120. In one example, the estimated frequency {overscore (f)}e is the mean B0 off-resonance frequency of the central r2M2×r2M2 pixels (0<r2≦1) in the selected M2×M2 matrix in the estimated B0 off-resonance frequency field map. While the mean B0 off-resonance frequency is described, it is to be appreciated that {overscore (f)}e may be selected in other manners.
At 1230, a water sub-image may be produced using {overscore (f)}e. In one example, the water sub-image may be computed using:
W′=(S0+S1 exp(−iφe))/2 [Equation 17], where
φe=2π{overscore (f)}e·τ [Equation 18].
At 1240, a 2D-FFT may be performed on the water sub-image to obtain Fourier data. At 1250, frequency demodulation is performed on the Fourier data with the frequency {overscore (f)}e to produce a demodulated data. While a frequency {overscore (f)}e is described, it is to be appreciated that other frequencies like fe may be employed.
At 1260, a 2D-IFFT may be performed on the demodulated data produced at 1250. Since the outer regions of the water sub-image may exhibit artifacts, in one example only the central r2M2×r2M2 pixels of a de-blurred water sub-image are retained for insertion into a final reconstructed image. Thus, at 1270, a portion of the de-blurred water sub-image may be returned to the locations in S0 and S1 from which it was acquired. Additionally, and/or alternatively, the portion may be stored in a new image separate from the original reconstructed images. At 1280, a determination is made concerning whether another block is to be decomposed and de-blurred. If the determination at 1280 is Yes, then processing may return to 1210, otherwise processing may conclude. Unlike conventional techniques, it is to be appreciated that method 1200 may be employed to reconstruct a portion of an image, rather than entire image, using a field map created at 1120.
In one example, methodologies are implemented as processor executable instructions and/or operations provided on a computer-readable medium. Thus, in one example, a computer-readable medium may store processor executable instructions operable to perform a method that includes acquiring two reconstructed MRI images of an item located in a B0 field, creating an estimated B0 off-resonance frequency field map using a BRORC-S2PD technique without performing multi-frequency testing and reconstructing a de-blurred water image using a BRORC-S2PD technique and the estimated B0 off-resonance frequency field map. The B0 off-resonance frequency map is related to the B0 field present when the MRI images were acquired. While the above method is described being provided on a computer-readable medium, it is to be appreciated that other example methods described herein can also be provided on a computer-readable medium.
At 1310, blurring artifacts may be reduced in the decomposed water and fat sub-images. At 1312, central matrices Wgc and Fgc may be extracted from the water sub-image and the fat sub-image. Signals in the central matrices Wgc and Fgc may then be used for frequency estimation as described by Equation 16. For example, at 1314, Tgc may be computed from the central matrix Wgc extracted from the water sub-image and Fgc extracted from the fat sub-image using, for example:
At 1316, an element in an initial estimated B0 off-resonance frequency field map can be established by setting its value to the off-resonance frequency fe computed for a central set of pixels associated with the region from which S0 and S1 were extracted. At 1318, a determination may be made concerning whether to process another block. If the determination is Yes, then processing may return to 1304. Otherwise processing may proceed to 1320 where a final B0 estimated off-resonance frequency field map may be created by applying a low pass filter to the initial estimated B0 off-resonance frequency map constructed by repetitions of the actions 1304 through 1316.
At 1330, sub-image matrices may again be extracted from corresponding locations in S0 and S1. At 1332, an estimated frequency for the region from which the sub-image matrices were extracted may be retrieved from the final estimated B0 off-resonance frequency field map. At 1334, a water sub-image may be produced from a sub-image matrix using a frequency like {overscore (f)}e described above. At 1336, a 2D-FFT may be performed on the water sub-image to obtain Fourier data and at 1338 a frequency demodulation may be performed on the Fourier data to produce a demodulated data. At 1340, a 2D-IFFT may be performed on the demodulated data produced at 1338 to produce a block of de-blurred data. At 1342, all or a portion of the de-blurred block may be returned to the locations in S0 and S1 from which it was extracted. At 1344, a determination is made concerning whether another block is to be decomposed and de-blurred. If the determination at 1344 is Yes, then processing may return to 1330, otherwise processing may conclude. Unlike conventional techniques, it is to be appreciated that method 1300 may be employed to reconstruct a portion of an image, rather than an entire image.
The MRI apparatus 1400 may include gradient coils 1430 configured to emit gradient magnetic fields like GS, GP and GR. The gradient coils 1430 may be controlled, at least in part, by a gradient coils supply 1440. The MRI apparatus 1400 may also include an RF antenna 1450 that is configured to generate RF pulses and to receive resulting magnetic resonance signals from an object to which the RF pulses are directed. Alternatively, separate RF transmission and reception coils can be employed. The RF antenna 1450 may be controlled, at least in part, by an RF transmission/reception unit 1460. The gradient coils supply 1440 and the RF transmission/reception unit 1460 may be controlled, at least in part, by a control computer 1470. In one example, the control computer 1470 may be programmed to perform methods like those described herein.
The magnetic resonance signals received from the RF antenna 1450 can be employed to generate an image, and thus may be subject to a transformation process like a two dimensional FFT that generates pixilated image data. The transformation can be performed by an image computer 1480 or other similar processing device. In one example, image computer 1480 may be programmed to perform methods like those described herein. The image data may then be shown on a display 1499.
While
Apparatus 1500 may also include a sub-image extraction logic 1520. The sub-image extraction logic 1520 may be configured to extract a sub-image from a reconstructed image stored in the image data store 1510. For example, original reconstructed images S0 and S1 may be N×N in size. The sub-image extraction logic 1520 may be configured to facilitate retrieving from the image data store 1510 a sub-image matrix of size M1×M1, where M1<N. The sub-image extraction logic 1520 may be configured to provide an extracted sub-image to a water-fat signal decomposition logic 1530. In some examples (e.g., apparatus 1700,
Apparatus 1500 may also include a water-fat signal decomposition logic 1530. The water-fat signal decomposition logic 1530 may be configured to decompose water-fat signals for the sub-images extracted by sub-image extraction logic 1520. In one example, the decomposition may depend, at least in part, on a guess frequency fg for the B0 frequency estimated for the region from which the sub-image was extracted. In one example, the original guess frequency fg may be zero. If a guess frequency fg close to the true frequency f of a particular sub-image region is available, then water-fat decomposition may be performed by water-fat signal decomposition logic 1530 using:
Wg′=(S0+S1 exp(−iφg))/2 [Equation 9], and
Fg′=(S0−S1 exp(−iφg))/2 [Equation 10], with
φg=2πfg·τ [Equation 11]
where Wg′ and Fg′ are decomposed water and fat sub-images. In one example, Wg′ and Fg′ may be stored in image data store 1510. In another example, Wg′ and Fg′ may be stored temporarily in the water-fat signal decomposition logic 1530 and/or passed to a frequency demodulation logic 1540. While a single water-fat signal decomposition logic 1530 is illustrated, it is to be appreciated that in some examples apparatus 1500 may include separate water and fat signal decomposition logics.
The frequency demodulation logic 1540 may be configured to reduce blurring artifacts in Wg′ to generate a de-blurred water image Wg from Wg′. For example, the frequency demodulation logic 1540 may be configured to perform a 2D-FFT on Wg′ to obtain Fourier data, to frequency demodulate the Fourier data with the frequency fg, and then to perform a 2D-IFFT on the demodulated Fourier data to reconstruct a water sub-image Wg. While a water sub-image is described, it is to be appreciated that a fat sub-image Fg may also be produced by frequency demodulation logic 1540.
Apparatus 1500 may also include a central matrix extraction logic 1550 that may be configured to extract central matrices (e.g., Wgc, Fgc) from the water sub-image Wg and fat sub-image Fg produced by the frequency demodulation logic 1540. Local frequency estimation may then be performed by a frequency estimation logic 1560. As part of local frequency estimation, Tgc may be computed by the frequency estimation logic 1560 from the extracted central matrices Wgc and Fgc.
Thus, in one example, a first estimate of the local B0 off-resonance frequency fe, may be determined by the frequency estimation logic 1560 using:
fe=fg−fd [Equation 14].
The frequency estimation logic 1560 may then update an initial map stored in an initial B0 off-resonance frequency field map data store 1570 by inserting fe at a location associated with the extracted sub-image. The value of fe may be relatively accurate if the region corresponding to Wgc and/or Fgc contains either predominantly water or fat tissue. However, frequency estimation may be unstable for voxels containing nearly equal water and fat signals. Therefore, apparatus 1500 may include a regularization function logic 1565 that is configured to perform a regularization function R associated with frequency estimation. In one example, an fe produced by the frequency estimation logic 1560 may be manipulated according to:
fe=fg−R·fd [Equation 16]
An example function R is illustrated in
Initial frequency map data store 1570 may store the initial estimated B0 off-resonance frequency map. The initial map may begin with no blocks for which a frequency has been estimated and may grow over time. In one example, the central r1M1×r1M1 pixels (0<r1≦1) of an M1×M1 matrix extracted by sub-image extraction logic 1520 and processed by water-fat signal decomposition logic 1530, frequency demodulation logic 1540, and frequency estimation logic 1560 are set to fe following the calculation of Equation 16. B0 frequencies for an entire image region or for a specific region(s) of an image may then be estimated by extracting other sub-images and processing them through the logics. However, subsequent blocks may benefit from the initial frequency estimation for the first block and other previously processed blocks. Thus, a region growing logic 1575 may facilitate performing block-based region growing actions to facilitate providing an estimated frequency fe for the guess frequency fg instead of an arbitrary value like 0. In one example, after the B0 frequency is estimated for a single block, the local B0 frequencies of the neighboring blocks may be estimated by the region growing logic 1575 using Equation 16. The output fe of the frequency-determined block may then be used by the frequency estimation logic 1560, the frequency demodulation logic 1540, the water-fat signal decomposition logic 1530, and so on, as fg for frequency estimation of the neighboring blocks.
Apparatus 1500 may also include a low pass filter logic 1580. The low pass filter logic 1580 may be configured to apply a low pass filter to an initial estimated B0 off-resonance frequency field map stored in data store 1570. The output of applying the low pass filter may be a final estimated B0 off-resonance frequency field map that may be stored in data store 1590. Once the final estimated B0 off-resonance frequency field map is produced, other components like those illustrated in apparatus 1700 (
The processor 1602 can be a variety of various processors including dual microprocessor and other multi-processor architectures. The memory 1604 can include volatile memory and/or non-volatile memory. The non-volatile memory can include, but is not limited to, ROM, PROM, EPROM, EEPROM, and the like. Volatile memory can include, for example, RAM, synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), and direct RAM bus RAM (DRRAM).
A disk 1606 may be operably connected to the computer 1600 via, for example, an input/output interface (e.g., card, device) 1618 and an input/output port 1610. The disk 1606 can include, but is not limited to, devices like a magnetic disk drive, a solid state disk drive, a floppy disk drive, a tape drive, a Zip drive, a flash memory card, and/or a memory stick. Furthermore, the disk 1606 can include optical drives like a CD-ROM, a CD recordable drive (CD-R drive), a CD rewriteable drive (CD-RW drive), and/or a digital video ROM drive (DVD ROM). The memory 1604 can store processes 1614 and/or data 1616, for example. The disk 1606 and/or memory 1604 can store an operating system that controls and allocates resources of the computer 1600.
The bus 1608 can be a single internal bus interconnect architecture and/or other bus or mesh architectures. While a single bus is illustrated, it is to be appreciated that computer 1600 may communicate with various devices, logics, and peripherals using other busses that are not illustrated (e.g., PCIE, SATA, Infiniband, 1394, USB, Ethernet). The bus 1608 can be of a variety of types including, but not limited to, a memory bus or memory controller, a peripheral bus or external bus, a crossbar switch, and/or a local bus. The local bus can be of varieties including, but not limited to, an industrial standard architecture (ISA) bus, a microchannel architecture (MSA) bus, an extended ISA (EISA) bus, a peripheral component interconnect (PCI) bus, a universal serial (USB) bus, and a small computer systems interface (SCSI) bus.
The computer 1600 may interact with input/output devices via i/o interfaces 1618 and input/output ports 1610. Input/output devices can include, but are not limited to, a keyboard, a microphone, a pointing and selection device, cameras, video cards, displays, disk 1606, network devices 1620, and the like. The input/output ports 1610 can include but are not limited to, serial ports, parallel ports, and USB ports.
The computer 1600 can operate in a network environment and thus may be connected to network devices 1620 via the i/o interfaces 1618, and/or the i/o ports 1610. Through the network devices 1620, the computer 1600 may interact with a network. Through the network, the computer 1600 may be logically connected to remote computers. The networks with which the computer 1600 may interact include, but are not limited to, a local area network (LAN), a wide area network (WAN), and other networks. The network devices 1620 can connect to LAN technologies including, but not limited to, fiber distributed data interface (FDDI), copper distributed data interface (CDDI), Ethernet (IEEE 802.3), token ring (IEEE 802.5), wireless computer communication (IEEE 802.11), Bluetooth (IEEE 802.15.1), Zigbee (IEEE 802.15.4) and the like. Similarly, the network devices 1620 can connect to WAN technologies including, but not limited to, point to point links, circuit switching networks like integrated services digital networks (ISDN), packet switching networks, and digital subscriber lines (DSL). While individual network types are described, it is to be appreciated that communications via, over, and/or through a network may include combinations and mixtures of communications.
Thus, apparatus 1700 may include a water sub-image logic 1735 configured to receive sub-image matrices of a size M2×M2 that are extracted by sub-image extraction logic 1720 from related locations in reconstructed images stored in image data store 1710. In one example, the sub-image extraction logic 1720 may be configured to extract sub-images that may be provided to either a water-fat signal decomposition logic 1730 and/or the water sub-image logic 1735.
The water sub-image logic 1735 may also be configured to separate water signals to produce a separated water sub-image W′. The separated water sub-image W′ may be stored in the water sub-image logic 1735 and/or may be provided to frequency demodulation logic 1740. In one example, both water signal separation and frequency demodulation may be performed for the extracted sub-images based on the frequency {overscore (f)}e. In one example, the water sub-image logic 1735 may produce a water sub-image using:
W′=(S0+S1 exp(−iφe))/2 [Equation 17], where
φe=2π{overscore (f)}e·τ [Equation 18].
The water sub-image W′ may exhibit blurring artifacts due to its B0 frequency. Therefore, de-blurring may be performed for the water sub-image W′ by the frequency demodulation logic 1740. In one example, the frequency demodulation logic 1740 may be configured to perform both processing like that described for frequency demodulation logic 1540 (
Thus, frequency demodulation logic 1740 may receive W′ and then perform a 2D-FFT on W′ to obtain Fourier data. The frequency demodulation logic 1740 may then perform a frequency demodulation on the Fourier data with the frequency {overscore (f)}e to produce a demodulated data. The frequency demodulation logic 1740 may then perform a 2D-IFFT on the demodulated data.
Since the outer regions of a sub-image matrix may exhibit artifacts, in one example only the central r2M2×r2M2 pixels of a de-blurred water sub-image are retained for insertion into a final reconstructed image. Thus, apparatus 1700 may include a central matrix extraction logic 1750. The central matrix extraction logic 1750 may be configured to select a portion of a de-blurred sub-image and to return it to the location from which it was acquired in the image stored in image data store 1710. In one example, a single central matrix extraction logic 1750 may be configured to perform processing performed by both central matrix extraction logic 1550 (
While example systems, methods, and so on, have been illustrated by describing examples, and while the examples have been described in considerable detail, it is not the intention of the applicants to restrict or in any way limit the scope of the appended claims to such detail. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the systems, methods, and so on, described herein. Additional advantages and modifications will readily appear to those skilled in the art. Therefore, the invention is not limited to the specific details, the representative apparatus, and illustrative examples shown and described. Thus, this application is intended to embrace alterations, modifications, and variations that fall within the scope of the appended claims. Furthermore, the preceding description is not meant to limit the scope of the invention. Rather, the scope of the invention is to be determined by the appended claims and their equivalents.
To the extent that the term “includes” or “including” is employed in the detailed description or the claims, it is intended to be inclusive in a manner similar to the term “comprising” as that term is interpreted when employed as a transitional word in a claim. Furthermore, to the extent that the term “or” is employed in the detailed description or claims (e.g., A or B) it is intended to mean “A or B or both”. When the applicants intend to indicate “only A or B but not both” then the term “only A or B but not both” will be employed. Thus, use of the term “or” herein is the inclusive, and not the exclusive use. See, Bryan A. Gamer, A Dictionary of Modern Legal Usage 624 (2d. Ed. 1995).
Portions of the claimed subject matter were developed with federal funding supplied under Federal Grants R01 CA81431 and R33 CA88144.