KR101531755B1 - Method and apparatus for dynamic image reconstruction using patch based low rank regularization in positron emission tomography - Google Patents

Abstract

A method and apparatus for image reconstruction are provided. An initial reconstructed image is calculated based on the plurality of sinograms, and a patch-based minimum-rank normalized image is generated based on the reconstructed image. The reconstructed image is updated based on the patch-based minimum-rank normalized image to generate a desired reconstructed image.

Description

TECHNICAL FIELD The present invention relates to a method and apparatus for reconstructing an image using patch-based minimum rank normalization, and more particularly to a method and apparatus for reconstructing an image using patch-

The following embodiments relate to Positron Emission Tomography (PET), and particularly to a method and apparatus for image reconstruction.

Tomographic imaging is an imaging technique that rotates a detector 180 ° or 360 ° so that a specific section of an object can be observed non-invasively without overlap with other adjacent sections.

A sinogram refers to a plurality of images acquired by tomography. The sinogram is reconstructed into a three-dimensional image. The observer can observe a specific cross-section of the photographed object through the reconstructed three-dimensional image.

The nuclear medicine tomographic image is an image in which the radiopharmaceutical administered to the subject is distributed in the body of the subject according to biochemical characteristics.

The amount of radioactive medicines administered into the body is limited by the reference value. Therefore, it is difficult for a high-resolution image to be reconstructed from a projection value recorded by a very small amount of photons.

When imaging a single layer using nuclear medicine imaging equipment, the noise in the signal is relatively strong compared to the intensity of the observed signal.

In particular, when dividing a frame into dynamic images, the amount of data in each frame is very small and the noise is much more increased.

Dynamic imaging in positron emission tomography is generally measured to observe the metabolism of a specific region of the body, and changes in metabolism can be estimated by the Time Activity Curve (TAC) of the region of the reconstructed image .

Generally, many changes occur within 3 minutes after injecting a radiopharmaceutical into the body. If the time interval of the measurement is at least 30 seconds, the ratio of noise becomes very high and accurate TAC can not be measured in many cases. Therefore, the parameter values representing the metabolism become inaccurate and the error becomes large.

Therefore, the ratio between the resolution and the noise of the reconstructed image is the most important factor in the metabolism measurement through the dynamic image.

The positron emission tomography reconstruction algorithm can use the maximum Likelihood Expectation Maximization (ML-EM) algorithm based on the poisson probability model. In dynamic image reconstruction, the noise of each frame image is too strong. Therefore, in the processing of the frame image, the noise of the frame image is reduced by applying gaussian blurring to the existing reconstruction algorithm once more.

However, despite the processing of Gaussian blurring, the noise ratio in the reconstructed image is still high, and the resolution of the reconstructed image is lowered due to the blurring effect of Gaussian blurring.

An embodiment of the present invention can provide an image reconstruction method and apparatus using patch-based minimum rank normalization.

An embodiment of the present invention can provide a method and apparatus for reconstructing an image using patch-based minimum rank normalization having an improved processing speed by processing operations in parallel.

According to one aspect of the present invention there is provided a method of reconstructing a reconstructed image comprising the steps of: receiving a plurality of sinograms generated by measuring an object at a different time from each other, which is performed by an image reconstruction device; Generating a patch-based minimum-rank normalized image based on the reconstructed image, and updating the reconstructed image based on the patch-based minimum-rank normalized image.

The initial reconstructed image may be a four-dimensional image generated by separately reconstructing a plurality of three-dimensional images generated based on the plurality of sinograms.

The calculating of the initial reconstructed image may reconstruct the plurality of three-dimensional images into the four-dimensional image using a probabilistic model-based expectation maximization algorithm.

The image reconstruction method may further include determining whether the updated reconstructed image converges.

If the reconstructed image does not converge, generating the patch-based minimum-rank normalized image and updating the reconstructed image may be performed repeatedly.

Wherein the step of determining whether the updated image converges comprises the steps of: setting a predetermined boundary value for determining whether the updated image converges; and determining whether the updated image is converged or not by comparing the reconstructed image before the update and the reconstructed image after the update And determining whether a mean square error of a difference between the threshold values is less than or equal to the threshold value.

The step of determining whether the updated image converges may determine that the reconstructed image converges if the mean square error is less than the threshold value.

Wherein the step of generating a patch-based minimum-rank normalized image based on the reconstructed image comprises the steps of: determining a patch as a reference in the reconstructed image; determining, based on the reference patch, Collecting a number of similar patches, generating a patch matrix by vectorizing the similar patches, obtaining eigenvalues of the patch matrix by performing an SVD operation on the patch matrix, performing a minimization operation on the eigenvalues , And generating the patch-based minimum-rank normalized image based on the minimized eigenvalues.

Wherein determining the reference patch comprises generating threads as many as the number of pixels of the reconstructed image and mapping the plurality of threads one-to-one to each patch in the center of each of the pixels can do.

The plurality of threads may be respectively processed by a plurality of cores of a graphics processing unit (GPU) of the image reconstruction apparatus.

Wherein the step of collecting the predetermined number of similar patches comprises the steps of: identifying all proximate patches present in the temporal and spatial axes within a predetermined search area from the reference patch in the reconstructed image; Calculating similarities between each of the near patches and extracting the predetermined number of similar patches of the near patches based on the calculated similarities.

The obtaining of the minimized eigenvalues may obtain the minimized eigenvalues by canceling eigenvalues less than or equal to a predetermined threshold value of the eigenvalues.

Wherein generating the patch-based minimum rank normalized image based on the minimized eigenvalues comprises generating a corrected matrix by multiplying the minimized eigenvalues by eigenvectors, Based minimum-normalized image; summing each correction patch of the correction patches at a position corresponding to each of the correction patches in the reconstruction image; And dividing the value of each pixel by the value of the correction patch added to each pixel.

According to another aspect of the present invention, there is provided an image processing apparatus including a receiving unit and a processing unit for receiving a plurality of sinograms generated by measuring a subject at different times from each other, Calculating a reconstructed image, generating a patch-based minimum-rank normalized image based on the initial reconstructed image, and updating the reconstructed image based on the patch-based minimum-rank normalized image.

According to another aspect of the present invention, there is provided an image processing apparatus including a receiving unit for receiving a plurality of generated synonyms by measuring a subject at different times from each other, a central processing unit (CPU) and a graphics processing unit (GPU) Wherein the central processing unit computes an initial reconstruction image based on the received sinograms, and based on the initial reconstruction image, generates a patch Based minimum rank normalized image and updates the reconstructed image based on the patch-based minimum-rank normalized image, wherein a plurality of cores of the graphics processing apparatus are operable to generate a plurality of threads used to calculate the initial reconstructed image An image reconstruction device is provided that is executed in parallel.

A method and apparatus for reconstructing an image in which the resolution of the reconstructed image is improved and the noise is reduced by using the patch-based minimum rank normalization is provided.

There is provided a method and an apparatus for reconstructing an image using patch-based minimum-rank normalization in which arithmetic processing is performed in parallel to reduce computation processing time.

1 is a structural diagram of an image reconstruction apparatus according to an embodiment of the present invention.
2 is a flowchart illustrating an image reconstruction method according to an embodiment of the present invention.
FIG. 3 is a flowchart illustrating a method of generating a patch-based minimum-rank normalized image according to an exemplary embodiment of the present invention.
4 is a flowchart illustrating a method of determining a reference patch in a reconstructed image according to an exemplary embodiment of the present invention
5 is a flowchart illustrating a method of collecting similar patches according to an exemplary embodiment of the present invention.
6 is a flowchart illustrating a method of generating a patch-based minimum-rank normalized image based on minimized eigenvalues according to an exemplary embodiment of the present invention.
7 is a flowchart illustrating a method for updating a reconstructed image according to an embodiment of the present invention.
FIG. 8 is a flowchart illustrating a method for determining whether an update image according to an exemplary embodiment of the present invention converges.

In the following, embodiments will be described in detail with reference to the accompanying drawings. Like reference symbols in the drawings denote like elements.

Various modifications may be made to the embodiments and may have various embodiments, and specific embodiments are illustrated in the drawings and described in detail in the description. It is to be understood, however, that the intention is not to limit the embodiments to the embodiments, but to include all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

The terms used in the examples are used only to illustrate specific embodiments and are not intended to limit the embodiments. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this embodiment belongs. Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the contextual meaning of the related art and are to be interpreted as either ideal or overly formal in the sense of the present application Do not.

In the following description of the present invention with reference to the accompanying drawings, the same components are denoted by the same reference numerals regardless of the reference numerals, and redundant explanations thereof will be omitted. In the following description of the embodiments, a detailed description of related arts will be omitted if it is determined that the gist of the embodiments may be unnecessarily blurred.

Hereinafter, the eigenvalues referred to in the first half of this document may be singular. For example, the terms "eigenvalue" and "singularity" may be used interchangeably.

1 is a structural diagram of an image reconstruction apparatus according to an embodiment of the present invention.

The image reconstruction apparatus 100 may include a receiving unit 110 and a processing unit 120.

The receiving unit 110 can receive a plurality of generated sinograms by measuring the object at different times from each other.

The receiving unit 110 may receive data indicating the generated sinogram through a wired or wireless network.

The processing unit 120 may include a central processing unit (CPU) 130 and a graphics processing unit (GPU) 140. The central processing unit 130 may include one or more cores 150. The graphics processing unit 140 may include one or more cores 160. For example, the graphics processing unit 140 may include tens to hundreds of cores 160.

The processing unit 120 may process the operations required for the image reconstruction apparatus 100 to perform image reconstruction.

The central processing unit 130 may process the operations required for the image reconstruction apparatus 100 to perform image reconstruction. The central processing unit 130 can process not only mathematical operations but also graphic operations. The central processing unit 130 can control the operation of the graphics processing unit 140. [

The graphics processing unit 140 may process operations required for the image reconstruction apparatus 100 to perform image reconstruction. The graphics processing unit 140 can process mathematical operations as well as graphic operations.

Each of the cores 150 or 160 may process the operations required for the image reconstruction apparatus 100 to perform image reconstruction in parallel. The frequency of data transmission and reception can be minimized in order to improve the operation speed of the parallel processing performed by the cores 150 or 160. [ For example, when the receiving unit 110 receives data generated from a positron emission tomography (CT) apparatus, the receiving unit 110 stores the sinograms required by the image reconstructing apparatus 100 to reconstruct the image, It can be received at one time before processing starts. After the operations for image reconstruction are processed, the reconstructed image can be received by the receiver 110 once after the processing of the operations is finished.

The processing of one operation performed by the core 150 or 160 may typically be completed within a few nanoseconds. It may take a time of several hundred nanoseconds or more for the read or write operation of the memory performed by the core 150 or 160. [ The time taken to process the operation can be reduced by processing the operations in parallel by the plurality of cores 150 or 160. [

2 is a flowchart illustrating an image reconstruction method according to an embodiment of the present invention.

In step 210, the receiving unit 110 may receive a plurality of generated sinograms by measuring the subject at different times from each other.

The sinograms may be real images, such as real images produced by measuring a subject by a positron emission tomograph. The sinograms can be three-dimensional images.

The receiving unit 110 may receive data indicating the generated sinogram. The data representing the sinograms may be transmitted from a positron emission tomograph or transmitted from a separate server for data provision. The data representing the sinograms may include information about the time axis of the received sinogram. For example, the receiving unit 110 may receive the sineograms for each frame.

In step 220, the processing unit 120 may calculate an initial reconstructed image based on the received sinograms. The initial reconstruction image may be a four-dimensional image generated by reconstructing a plurality of three-dimensional images generated based on a plurality of sinograms individually on a time-by-time basis.

For example, the plurality of sinograms may correspond to a plurality of three-dimensional images, respectively. That is, the initial reconstruction image may be a four-dimensional image generated by reconstructing each of the plurality of sinograms, which are three-dimensional images, individually by time.

In step 220, the processing unit 120 may reconstruct a plurality of three-dimensional images into a four-dimensional image using a probabilistic model-based expectation maximization algorithm.

The computation of the probability maximization algorithm based on the probability model performed in step 220 can be expressed by Equation 1 below.

Here, x can represent an image. y may represent a sinogram. a can represent a system function.

The updating process of the image is repeated, and k can represent the number of iterations. In other words, k may be the number of times the step 220 and the step 240 were performed or the number of times the step 240 was performed.

n it may be an index that points to the n-th voxel (voxel) or the n-th voxel.

s can be a specific time. m may be an exponent representing the mth detector.

x _ns ^{EM ( k +1)} may be a probabilistic model-based expectation update update value of the unknown image at the n- th voxel and time s in the k + 1th iteration.

x _ns ^{( k )} may be the nth voxel in the kth iteration and the unknown image in the time s.

y _ms may be the measurement value of the mth detector at time s . a _mn May be the probability that the photons emitted from the nth voxel will be detected at the mth detector position.

n ' N ' Lt; RTI ID = 0.0 > n & Lt; RTI ID = 0.0 > voxel. ≪ / RTI >

x _n 's ^(k) may be the unknown image at the n ' th voxel and at time s in the k th iteration.

The operations required to generate the initial reconstruction image using the probabilistic model based expectation maximization algorithm are performed by the cores 150 of the central processing unit 130 or the cores 160 of the graphics processing unit 140 Lt; / RTI >

For example, the plurality of cores 150 of the central processing unit 130 may execute a plurality of threads used in parallel to calculate an initial reconstruction image.

For example, each of the cores 150 may correspond to each pixel of time-based three-dimensional images received by the receiver 110, Can be processed in parallel.

Alternatively, the operations required to generate the initial reconstruction image using the probabilistic model based expectation maximization algorithm may be processed in parallel by the cores 160 of the graphics processing unit 140.

For example, the plurality of cores 160 of the graphics processing unit 140 may execute a plurality of threads used in parallel to compute an initial reconstructed image.

For example, each of the cores 160 may correspond to each pixel of the temporal three-dimensional images received by the receiver 110, Can be processed in parallel.

In step 230, the central processing unit 130 may generate a patch-based minimum-rank normalization image based on the reconstructed image.

The reconstructed image for generating the patch-based minimum-rank normalized image may be the initial reconstructed image generated in step 220. Alternatively, the reconstructed image for generating the patch-based minimum-rank normalized image may be a reconstructed image generated after one or more steps 240 and 250 described below are performed.

The patch-based minimum-rank normalized image may be an image generated based on patches obtained from the reconstructed image.

The patch may be a block of constant size in the reconstruction image. Using the patches obtained from the reconstructed image, a patch-based minimum-rank normalized image can be generated. An algorithm for updating the reconstructed image based on the patch-based minimum-rank normalized image can be used for noise reduction of the reconstructed image.

An algorithm for reducing the noise of the reconstructed image on a patch-by-patch basis can provide a more stable and improved performance than other algorithms for noise reduction of the reconstructed image, for example, algorithms for reducing the noise of the reconstructed image on a pixel-by-pixel basis.

The processing unit 120 may perform step 230 by repeating the processing of the independent operations on each of the patches obtained from the reconstructed image. Independent operations for each of the patches obtained from the reconstructed image can be processed in parallel by each of the cores 150 of the central processing unit 130. Alternatively, independent operations for each of the patches obtained from the reconstructed image may be processed in parallel by the respective cores 160 of the graphics processing unit 140.

For example, each of the patches obtained from the reconstructed image may be software-linked to each of the threads of the graphics processing unit 140, or may be software-linked to each of the threads of the central processing unit 130. [

The operations for each of the patches may be processed in parallel by each of the threads of the graphics processing unit 140. [ Alternatively, operations for each of the patches may be processed in parallel by each of the threads of the central processing unit 130. [

Alternatively, operations for each of the patches may be performed continuously by the central processing unit 130 physically.

Alternatively, operations for each of the patches may be performed in parallel by each of the cores 160 of the graphics processing unit 140. [ Alternatively, operations for each of the patches may be processed in parallel by each of the cores 160 of the central processing unit 140. [

In step 240, the processing unit 120 may update the reconstructed image based on the patch-based minimum-rank normalization image generated in step 230.

The reconstructed image updated in step 240 may be the reconstructed image generated in step 220. Alternatively, the reconstructed image to be updated may be an updated reconstructed image after step 240 and step 250 described below are performed more than once.

Step 240 may be repeatedly performed on the reconstructed image. The repeated execution of step 240 of updating the reconstructed image may depend on the outcome of performing step 250, which will be described later.

In step 250, the processing unit 120 may determine whether the updated reconstructed image generated by performing step 240 is converged. For example, the processing unit 120 may determine that the updated reconstructed image converges or does not converge. If the reconstructed image does not converge according to the determination of the processing unit 120, the step 230 of generating a patch-based minimum-rank normalized image and the step 240 of updating the reconstructed image may be repeatedly performed. That is to say, the performance of steps 230 and 240 may be repeated until the updated reconstructed image generated as a result of performing step 240 converges.

When the updated image converges, the updated image may be a desired reconstructed image.

If the updated image converges, steps 230 and 240 may not be repeated. It can be determined whether or not the updated image is finally converged by the processing unit 120. [ If it is determined that the updated image finally converges, the procedure of the method may be terminated.

FIG. 3 is a flowchart illustrating a method of generating a patch-based minimum-rank normalized image according to an exemplary embodiment of the present invention.

2, the processing unit 120 may perform a step 230 of generating a patch-based minimum-rank normalization image based on the reconstructed image. Step 230 may include steps 310 through 360 described below.

In step 310, the processing unit 120 may determine a patch that is a basis for generation of the patch-based minimum-rank normalization image.

Depending on the reconstructed image for generating the patch-based minimum-rank normalized image, the reference patch may be one or more for each pixel of the reconstructed image. For example, there may be multiple reference patches for the same pixel of the reconstructed image.

The reference patches can be acquired in space. For example, the reference patches may be two-dimensional patches or three-dimensional patches. If the reconstructed image is a dynamic image, the reference patches may be acquired on the time axis. For example, a reference patch may be obtained for each frame of a dynamic image.

The reference patches may be reference patches to obtain similar patches of step 320 described below.

In step 320, the processing unit 120 may collect a predetermined number of similar patches that are most similar to the reference patch obtained in step 310. [

When the reconstructed image is divided into a plurality of patches, similar patches similar to the reference patch may exist due to the self-similarity characteristic of the image.

Similar patches can be obtained in the spatial axis. For example, similar patches may be two-dimensional or three-dimensional patches. If the reconstructed image is a dynamic image, similar patches may be acquired on the time axis. For example, a similar patch may be obtained for each frame of the dynamic image.

Similar patches similar to the reference patch can be used for noise reduction of the reconstructed image. Similar patches similar to the reference patch can be applied to the reconstructed image. In a reconstructed image with similar patches, the boundary line or shape in the reconstructed image before application of the similar patch can be maintained in the reconstructed image after application of the similar patch. The noise in the reconstructed image after application of the similar patch can be reduced as compared with the noise in the reconstructed image before application of the similar patch, as the boundary line or shape remains intact. The manner in which similar patches are applied is described in detail below.

At step 330, the processing unit 120 may generate a patch matrix by vectoring similar patches. Similar patches can be two-dimensional or three-dimensional patches. Each of the similar patches may be transformed into a vector. For example, the processing unit 120 may convert similar patches into two-dimensional or three-dimensional vectors, respectively.

Each column of the patch matrix may consist of each of the vectors into which similar patches are transformed. The processing unit 120 may construct vectors as rows of a patch matrix. Similar patches obtained at the same time can constitute columns of one patch matrix, respectively. For example, the processing unit 120 may obtain similar patches from each of the frames. The processing unit 120 may generate a patch matrix corresponding to each of the frames by using similar patches obtained from each of the frames for which similar patches have been acquired for each frame.

Similar patches obtained on the basis of the same reference patch can constitute the columns of the same patch matrix, respectively. For example, each set of similar patches obtained on the basis of each of the reference patches may generate the same patch matrix according to the reference patch.

As described above, a patch matrix can be generated by constructing the rows of the patch matrix with vectorized similar patches. As the patch matrix is generated, the processing unit 120 may perform an SVD operation to obtain the eigenvalues of the patch matrix.

In step 340, the processing unit 120 may obtain the eigenvalues of the patch matrix by performing an SVD operation on the patch matrix.

Each column of the patch matrix to which the SVD operation is applied may be a two-dimensional or three-dimensional similar patch converted into a two-dimensional or three-dimensional vector.

The frames of the dynamic image can be divided in order. k can represent the order of the frames of the dynamic image. k may be an integer of 1 or more. The SVD operation for the patch matrix in the k-th frame can be defined as Equation (2) below.

Here, V _p ^{( k )} may be a patch matrix. The columns of V _p ^{( k )} may be vectors that are formed by vectoring similar patches obtained on the basis of the patch that is the pth reference in the kth iteration.

p may be an integer of 1 or more.

L may be a square orthogonal matrix.

[Sigma] may be a diagonal matrix. For example,? May be a matrix where the values of the elements on the diagonal are 0 or positive, and the values of the elements that are not on the diagonal are all zero. The elements on the diagonal line may be elements having the same row number and column number.

Each of the elements of Σ can be the singular value of V _p ^{( k )} . The number of singular values in Σ number of the element, and V _p ^(k) may be equal to each other.

U ^H May be a conjugate transpose matrix of the matrix U and may be a square unitary matrix.

Eigenvalues of the patch matrix can be obtained by decomposing the patch matrix into the above-described matrices using Equation (2).

Each of the operations of Equation (2) for all of the patch matrices may be processed in parallel by the cores 150 of the central processing unit 130. [ Alternatively, each of the operations of Equation (2) for all of the patch matrices may be processed in parallel by the cores 160 of the graphics processing unit 140.

In step 350, the processing unit 120 may obtain the minimized eigenvalues by performing a minimization operation on the eigenvalues obtained through the SVD operation. Minimization operations on eigenvalues may be operations that minimize the number of eigenvalues.

The processing unit 120 can reduce the noise of the reconstructed image on a patch-by-patch basis by minimizing the rank of the patch matrix. That is, an algorithm for reducing the noise of the reconstruction image on a patch-by-patch basis by applying reference patches and similar patches acquired from the reconstruction image to the reconstruction image can be performed by minimizing the rank of the patch matrix.

As described above, the rank of the patch matrix may be the number of eigenvalues of the rank of the patch matrix. That is, the minimization operation on the eigenvalues of the patch matrix may be an operation that minimizes the rank of the patch matrix. The operation that minimizes the rank of the patch matrix may be an operation that normalizes the rank of the patch matrix.

The first patch matrix generated from the first reconstructed image having relatively more noise includes a relatively smaller number of eigenvalues that are relatively smaller in size than the second patch matrix generated from the second reconstructed image having relatively less noise can do. The eigenvalues of relatively smaller magnitudes that the first patch matrix further includes may be eigenvalues less than or equal to a predetermined threshold value.

The processing unit 120 may perform a minimization operation on eigenvalues by canceling eigenvalues less than or equal to a predetermined threshold value included in the patch matrix. For example, the processing unit 120 may obtain minimized eigenvalues by erasing eigenvalues less than a predetermined threshold value among eigenvalues of the patch matrix generated from the reconstructed image.

An operation for canceling eigenvalues equal to or less than a predetermined boundary value among the eigenvalues of the patch matrix can be expressed by Equation (3) and Equation (4) below.

Here, W _p ^{( k +1)} may be a matrix having eigenvalues minimized by eliminating eigenvalues less than a predetermined threshold value among eigenvalues of the patch matrix. The columns of the patch matrix may be vectors generated by vectorizing similar patches obtained on the basis of the patch of the pth reference in the ( k + 1) th iteration.

p may be an integer of 1 or more.

L may be a square orthogonal matrix.

Shrink _ν ( Σ , μ ) can be an element by element singular value shrink operator for Σ . For example, shrink _ν ( Σ , μ ) can be a matrix of the same size as Σ, and can be computed for each element.

In shrink _ν ( Σ , μ ), an operation that truncates the boundary value determined by μ and υ can be performed for each element. In this case, a value smaller than 0 in shrink _ν ( Σ , μ ) can be zero.

[Sigma] may be a diagonal matrix. For example ,? May be a matrix where the values of the elements on the diagonal are 0 or positive, and the values of the elements that are not on the diagonal are all zero. The elements on the diagonal line may be elements having the same row number and column number.

Each element of shrink _ν ( Σ , μ ) can be the singular value of the matrix W _p ^{( k +1)} . The number of elements of shrink _ν ( Σ , μ ) and the number of singular values of matrix W _p ^{( k +1)} can be the same.

v may be a predetermined value to make the reconstruction result concave prior. For example, v may be 0.01 or more and 0.1 or less.

mu may be a factor related to the quality of the image. μ may be a value predetermined selected by trial and error (trial and error) method in consideration of the strength of the patch.

U ^H May be the conjugate transpose matrix of the matrix U. U ^H May be a square-unitary matrix.

W _p V _p And Σ values may be different, and W _p V _p The noise can be reduced.

Each of the operations of Equation 3 for all of the patch matrices may be processed in parallel by the cores 150 of the central processing unit 130. [ Alternatively, each of the operations of Equation (3) for all of the patch matrices may be processed in parallel by the cores 160 of the graphics processing unit 140.

As used in the above-described Equation 3, shirink _υ function being among the eigenvalues of the matrix patch is used to erase a specific value equal to or less than a predetermined threshold value may be expressed by Equation 4 below.

Here, t may be an input variable input to the shirink operator.

v may be a predetermined value to make the reconstruction result concave prior. For example, v may be 0.01 or more and 0.1 or less.

mu may be a factor related to the quality of the image. μ may be a value predetermined selected by trial and error (trial and error) method in consideration of the strength of the patch.

The processing unit 120 can eliminate eigenvalues less than a predetermined threshold value among the eigenvalues of the patch matrix by applying the operation of Equation (4) described above to the operation of Equation (3). That is to say, step 350 can be performed by the processing unit 120 applying the operation of Equation 3 and the operation of Equation 4 to the patch matrix.

At step 360, the processing unit 120 may generate a patch-based minimum-rank normalization image based on the minimized eigenvalues.

The processing unit 120 may generate the patch-based minimum-rank normalized image by applying the similar patches obtained in the above-described step 350 to the reconstructed image.

The generated patch-based minimum-rank normalization image may be used for performing the steps 240 and 250 of FIG. 2 described above. For example, the patch-based minimum-rank normalization image generated in step 360 may be a patch-based minimum-rank normalized image generated by performing step 230 after determining that the reconstructed image does not converge in step 250 have.

4 is a flowchart illustrating a method of determining a reference patch in a reconstructed image according to an exemplary embodiment of the present invention.

The above-described step 310 in FIG. 3 may include the steps 410 to 420 described below.

At step 410, the processing unit 120 may generate as many threads as the number of pixels of the reconstructed image to determine a reference patch in the reconstructed image. The number of generated threads may be equal to the number of reference patches.

The generated plurality of threads can be respectively processed by the plurality of cores 160 of the graphic processing unit 140 of the image reconstruction apparatus 100. [

In step 420, the processing unit 120 may associate the generated plurality of threads one-to-one with each of the pixels arranged in the center. For example, each of the reference patches may correspond to one of a plurality of generated threads. The reference patches and the generated plurality of threads can correspond one to one.

That is, an operation or code for processing each patch of the reference patches may be software-linked to a thread of the graphics processing unit 140 or a thread of the central processing unit 130. [ Operations or codes for processing the reference patches may be processed in parallel by the threads of the graphics processing unit 140. [ Alternatively, operations or codes for processing the underlying patches may be processed in parallel by the threads of the central processing unit 130. [

Alternatively, the operation processing for the threads corresponding to the reference patches can be performed physically continuously by the processing unit 120. [

Or operations for threads corresponding to the underlying patches may be processed in parallel by the cores 160 of the graphics processing unit 140 or the cores 150 of the central processing unit 130. [

Each of the cores 150 or 160 may correspond to a pixel present at the center of each of the reference patches.

5 is a flowchart illustrating a method of collecting similar patches according to an exemplary embodiment of the present invention.

The above-described step 320 in FIG. 3 may include the steps 510 to 530 described below.

In step 510, the processing unit 120 may identify all proximate patches present in the temporal and spatial axes within a predetermined search range from the reference patch in the reconstructed image.

The predetermined search area may be a predetermined area existing on the time axis and / or the space axis. The processing unit 120 can determine the range of a predetermined search area by determining whether the similarity between the patches as the reference is within a predetermined threshold value.

In the time axis, a predetermined search area may be divided into frames.

In the spatial axis, the range of the predetermined search area can be determined based on the distance from the center of the reference patch. A pixel may be located at the center of the reference patch.

The processing unit 120 can identify all nearby patches that are within the range of a predetermined search area determined in the time axis and / or the spatial axis, based on the reference patches.

In step 520, the processing unit 120 may calculate the similarities between each of the reference patch and the adjacent patches.

As described above, the reference patches obtained in the reconstruction image can be vectorized. For example, the reference patches can be converted into two-dimensional or three-dimensional vectors.

The similarity between the reference patches and each of the proximity patches identified in step 510 may be a number representing the similarity between the vectorized patches. For example, the processing unit 120 may determine the similarity by calculating the distance (L2-distance) between each of the patches being the vectorized reference and the adjacent patches identified in the vectorized step 510. [

In step 530, the processing unit 120 may extract the predetermined number of similar patches of the proximity patches based on the calculated similarities.

The processing unit 120 may preset a predetermined number of proximity patches extracted as similar patches of the proximity patches identified in step 510. [ In other words, the processing unit 120 can preset the number of similar patches. The processing unit 120 may allocate the amount of memory necessary for the SVD operation processing of Equation (2) in accordance with the number of similar pseudo-patches set in advance.

The processing unit 120 can determine the number of adjacent patches extracted as a similar patch according to a predetermined threshold value of similarity that can be preset by the processing unit 120. [

The processing unit 120 may extract proximate patches extracted from the proximity patches identified in step 510 as similar patches in the order of high degree of similarity.

For example, the processing unit 120 may extract patches whose similarity to the vectorized reference patch is less than or equal to a predetermined threshold value among the identified nearby patches.

For example, when a predetermined number of proximate patches extracted as similar patches by the processing unit 120 are preliminarily set, the processing unit 120 sets the proximity patches, which are vectorized references, It is possible to extract as many patches as the number of patches.

6 is a flowchart illustrating a method of generating a patch-based minimum-rank normalized image based on minimized eigenvalues according to an exemplary embodiment of the present invention.

Step 360 described above in FIG. 3 may include steps 610 through 640 described below.

In step 610, the processing unit 120 may generate a corrected matrix by multiplying eigenvectors with the minimized eigenvalues.

As described above in step 350 of FIG. 3, the processing unit 120 can erase eigenvalues below a predetermined threshold value by using Equations (3) and (4) By erasing, the eigenvalues of the patch matrix can be minimized. The processing unit 120 may also use the minimized eigenvalues to obtain minimized eigenvectors for the patch matrix. Here, the minimized eigenvectors and the minimized eigenvalues can be associated one-to-one. That is to say, each of the minimized eigenvectors can pair each of the minimally eigenvalues with each other. The processing unit 120 may obtain the vectors by multiplying the minimized eigenvectors and the minimized eigenvalues that form the pair of minimized eigenvectors and the minimized eigenvalues. Each of the obtained vectors may constitute each column of the calibrated matrix generated in step 610. That is to say, the processing unit can generate the corrected matrix by using the obtained vectors as columns, and the columns of the corrected matrix and the obtained vectors can correspond one-to-one.

In step 620, the processing unit 130 may convert the columns of the corrected matrix into correction patches for generation of a patch-based minimum-rank normalized image.

Each column of the corrected matrix may be a vector for generating a patch-based minimum-rank normalization image. The vector constituting each column of the corrected matrix may be a two-dimensional or three-dimensional vector. The two-dimensional or three-dimensional vector constituting each column of the corrected matrix can be converted into a two-dimensional or three-dimensional correction patch. For example, if the corrected matrix is a matrix having columns of two-dimensional vectors, each column of the corrected matrix may be transformed into two-dimensional correction patches. If the corrected matrix is a matrix having columns of three-dimensional vectors, each column of the corrected matrix may be transformed into three-dimensional correction patches.

In step 630, the processing unit 120 may add each correction patch of correction patches to a location corresponding to each correction patch in the reconstruction image.

In step 640, the processing unit 120 may divide the value of each pixel for each pixel in the reconstruction image by the value of the correction patch added to each pixel.

As with a plurality of similar patches obtained by performing steps 510 to 530 for a single reference patch, for a single reference patch, a plurality of corrections obtained through step 620 Patches may exist. A plurality of similar patches may exist within a predetermined search range centered on one reference patch, so that a plurality of patches applied to some pixels of the reconstruction image may be overlapped. Likewise, since there may be a plurality of correction patches within a predetermined search range for one reference patch, patches may be applied overlapping with some pixels of the reconstruction image.

The processing unit 120 can generate a desired patch-based minimum-rank normalized image by correcting the values of correction patches added to each pixel as if the same number of patches were applied to each pixel of the reconstructed image . For example, the processing unit 120 may correct the values of correction patches that are applied redundantly to each pixel of the reconstructed image, just as one correction patch is applied to each pixel of the reconstructed image.

For example, the processing unit 120 may divide the value of each pixel by the number of correction patches added to each pixel for each pixel of the reconstructed image to which the correction patch is applied. The number of correction patches divided for each pixel may be the number of times the correction patches are applied to each of the pixels.

7 is a flowchart illustrating a method for updating a reconstructed image according to an embodiment of the present invention.

Step 240 described above with reference to FIG. 2 may include steps 710 through 730 described below.

The patch-based minimum-rank normalized image generated in step 230 of FIG. 2 may be input to the processing unit 120 for updating.

At step 720, the processing unit 120 may generate a reconstructed image using a probabilistic model based expectation maximization algorithm.

The probabilistic model based expectation maximization algorithm used in step 220 of FIG. 2 may be applied to step 720. The reconstructed image generated in step 720 may be the initial reconstructed image generated in step 220 of FIG. Alternatively, the reconstructed image generated in step 720 may be an updated reconstructed image generated after the steps 230 to 250 of FIG. 2 are performed more than once.

In step 730, the processing unit 120 may update the reconstructed image by using the input patch-based minimum-rank normalization image and the probability model-based expectation maximization algorithm.

The operation for updating the reconstructed image by using the patch-based minimum-rank normalized image and the probability-model-based expectation maximization algorithm can be expressed by the following equation (5).

And

Here, n may be an index representing an n- th voxel.

s can be a specific time. m may be an exponent representing the m- th detector.

x _ns ^{( k +1)} may be the nth voxel in the k + 1th iteration and the unknown image at time s . ^EM x _ns ^{(k +1)} may be a value ML-EM updated at k + 1 and n-th voxel time s of the second repeat. a _mn May be the probability that the photons emitted from the nth voxel will be detected at the mth detector position.

mu may be a factor related to the quality of the image. These μ may be a value predetermined by trial and error (trial and error) method in consideration of the strength of the patch.

p may be an exponent representing a patch that is a p- th reference.

lambda may be to impose a balance factor between log-likelihood and low-rank regularization conditions.

w _{p , ns} ^{( k +1)} has contributions for the nth voxel at time s after a low-rank constrained shrinkage operation of Equation 2 in the ^{( k} + 1) and may represent a specific element of the pth patch.

The processing unit 120 can select the value of ? To satisfy the following equation (6) for the constant value c .

lambda _p may be lambda for the patch that is the pth reference.

I _{ns Lt;} RTI ID = 0.0 > x _ns Lt; RTI ID = 0.0 > a < / RTI >

a _mn May be the probability that the photons emitted from the nth voxel will be detected at the mth detector position.

Σ _{p∈I_ ns} w _p May be the final w _{p , n s} .

In step 250 of FIG. 2, if the processing unit 120 determines in step 730 that the updated image has not converged, the updated image is used as a reconstructed image for performing the steps 230 to 240 . If the processing unit 120 determines in step 730 that the updated image is converged, the updated image may be a desired reconstructed image.

FIG. 8 is a flowchart illustrating a method for determining whether an update image according to an exemplary embodiment of the present invention converges.

Step 250 described above with reference to FIG. 2 may include steps 810 and 820 described below.

In step 810, the processing unit 120 may set a predetermined boundary value for determining whether the updated image converges.

In step 820, the processing unit 120 may determine whether the updated image converges by comparing the difference between the set threshold value and the reconstructed image before the update and the reconstructed image after the update.

For example, the predetermined boundary value may be a mean square error of a predetermined value or less.

In step 820, the processing unit 120 may perform a step of determining whether the mean square error of the difference between the reconstructed image before the update and the reconstructed images after the update is less than or equal to the threshold value have.

The central processing unit 130 may determine that the reconstructed image converges if the mean square error between the reconstructed image before the update and the reconstructed image after the update is less than the threshold value.

In the foregoing description, steps described as being capable of being performed by the processing unit 120 may be replaced by those that the central processing unit 130 or the graphics processing unit 140 can perform. That is, the processing unit 120, the central processing unit 130, and the graphic processing unit 140 may be used interchangeably.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

100: Image reconstruction device
110:
120:
130: central processing unit
140: graphics processing unit
150: Core
160: Core

Claims (13)

The image reconstruction device,
The method comprising: receiving a plurality of generated sinograms by measuring a subject at different times;
Calculating an initial reconstruction image based on the received sinograms;
Generating a patch-based minimum-rank normalized image based on the reconstructed image; And
Updating the reconstructed image based on the patch-based minimum-rank normalization image
And reconstructing the image. The method according to claim 1,
Wherein the initial reconstructed image is a 4-dimensional image generated by separately reconstructing a plurality of 3-dimensional images generated based on the plurality of sinograms by time. 3. The method of claim 2,
Wherein the step of calculating the initial reconstructed image comprises:
And reconstructing the plurality of three-dimensional images into the four-dimensional image using an expectation maximization algorithm based on a probability model. The method according to claim 1,
Determining whether the updated reconstructed image converges;
Further comprising:
Wherein if the reconstructed image does not converge, generating the patch-based minimum-rank normalized image and updating the reconstructed image are repeatedly performed. 5. The method of claim 4,
Wherein the step of determining whether the updated reconstructed image converges comprises:
Setting a predetermined boundary value for determining whether the updated reconstructed image converges; And
Determining whether a mean square error of a difference between the reconstructed image before the update and the reconstructed image after the update is less than or equal to the threshold value
Lt; / RTI >
Wherein the step of determining whether the updated reconstructed image converges comprises determining that the reconstructed image converges if the mean square error is less than or equal to the threshold value. The method according to claim 1,
Wherein the step of generating a patch-based minimum-rank normalized image based on the reconstructed image comprises:
Determining a reference patch in the reconstructed image;
Collecting, based on the reference patch, a predetermined number of similar patches most similar to the reference patch;
Generating a patch matrix by vectorizing the similar patches;
Obtaining eigenvalues of the patch matrix by performing an SVD operation on the patch matrix;
Obtaining minimized eigenvalues by performing a minimization operation on the eigenvalues;
Generating the patch-based minimum-rank normalized image based on the minimized eigenvalues
And reconstructing the image. The method according to claim 6,
Wherein the step of determining the reference patch comprises:
Generating threads as many as the number of pixels of the reconstructed image; And
Associating the plurality of threads with a one-to-one correspondence to patches each of which is centrally located
And reconstructing the image. 8. The method of claim 7,
Wherein the plurality of threads are each processed by a plurality of cores of a graphics processing unit (GPU) of the image reconstruction apparatus, The method according to claim 6,
Wherein the collecting of the predetermined number of similar patches comprises:
Identifying all proximate patches in the temporal and spatial axes within a predetermined search range from the reference patch in the reconstructed image;
Calculating similarities between the reference patch and each of the near patches; And
Extracting the predetermined number of similar patches of the adjacent patches based on the calculated similarities;
And reconstructing the image. The method according to claim 6,
Wherein the obtaining of the minimized eigenvalues comprises:
And obtaining the minimized eigenvalues by erasing eigenvalues less than or equal to a predetermined threshold value of the eigenvalues. The method according to claim 6,
Wherein generating the patch-based minimum-rank normalized image based on the minimized eigenvalues comprises:
Generating a corrected matrix by multiplying the minimized eigenvalues by eigenvectors;
Transforming the columns of the corrected matrix into correction patches for generation of a patch-based minimum-rank normalized image;
Summing each correction patch of the correction patches at a position corresponding to each correction patch in the reconstruction image;
Dividing the value of each pixel for each pixel in the reconstructed image by the value of the correction patch added to each pixel
And reconstructing the image. A receiving unit for receiving a plurality of generated sinograms by measuring a subject at different times; And
Processing unit
/ RTI >
Wherein the processor calculates an initial reconstructed image based on the received sinograms, generates a patch-based minimum-rank normalized image based on the initial reconstructed image, and based on the patch-based minimum-rank normalized image, And the image reconstruction unit updates the reconstructed image. A receiving unit for receiving a plurality of generated sinograms by measuring a subject at different times;
A central processing unit (CPU); And
A graphics processing unit (GPU)
Lt; / RTI >
The graphics processing device
The plurality of cores
/ RTI >
The central processing unit calculates an initial reconstruction image based on the received sinograms, generates a patch-based minimum-rank normalization image based on the initial reconstruction image, and generates a patch-based minimum-rank normalization image Updating the reconstructed image based on the reconstructed image,
Wherein a plurality of cores of the graphics processing unit execute in parallel a plurality of threads used to compute the initial reconstruction image.

Images