Successive approximate image reconstruction method, successive approximate image reconstruction program and tomography device

Abstract

Provided are a successive approximation image reconstruction method, a successive approximation image reconstruction program, and a tomography apparatus, which can shorten the calculation time and efficiently perform reconstruction even when the reconstruction of the image is restarted when the image is reconstructed using the successive approximation method. In the successive approximation image reconstruction method, the following configuration is adopted: when an image with a repetition number of 100 is obtained by the initial image reconstruction process, if the image quality of the reconstructed image is insufficient, when the image reconstruction is restarted, the reconstructed image and state variables at the end of the reconstruction of the image with a repetition number of 100 are read, and the image reconstruction is restarted.

Description

Technical Field

[0001] The present invention relates to a successive approximation image reconstruction method, a successive approximation image reconstruction program and a tomography device for reconstructing an image using a successive approximation method. Background Art

[0002] For example, when performing image reconstruction in an X-ray CT (Computed Tomography) device as a tomography device, filtered back projection (FBP) has been used as a standard image reconstruction method in the past. In contrast, in recent years, due to the improvement of computer performance, etc., research and practical application of image reconstruction using the successive approximation method have been developed. When using the successive approximation method, in order to reduce false images caused by various factors and reflect complex physical models or known knowledge, various methods have been proposed so far (see Patent Document 1, Patent Document 2, Non-Patent Document 1).

[0003] Such a method can be considered as a successive approximation method based on objective function maximization. This method maximizes the objective function F represented by the following (Formula 1) to obtain a reconstructed image.

[0004] [Formula 1]

[0005] F(μ,y)=D(μ,y)+βR(μ)…(Formula 1)

[0006] Here, μ in the above (Formula 1) is a reconstructed image vector, and y is projection data. In addition, D is called a "data item" and the like, and is a term that indicates the degree of fit with the measured data, and is defined by the likelihood calculated from the measured projection (measured projection data obtained by the X-ray detector) and the estimated parameters (the estimated image estimated in the above (Formula 1)). In addition, μ and y are vectors, so they are expressed in bold.

[0007] In addition, R is generally referred to as a "penalty term" or the like, and reflects the rationality of the estimated parameters (estimated image). In this specification, R is referred to as a "rationality term" for convenience. In addition, β is a coefficient for controlling the strength of the rationality term R, and is determined empirically.

[0008] In the actual calculation of the above (Formula 1), an optimization algorithm such as the gradient descent method or the Newton method is used. In addition, in order to avoid falling into a local solution, there are also cases where a combined optimization method such as a genetic algorithm or an annealing method is combined. When the gradient descent method is used as the optimization algorithm, the update formula of the reconstructed image of the above objective function is expressed as follows (Formula 2).

[0009] [Formula 2]

[0010]

[0011] The α in the above (Formula 2) is called the step width, which has the function of controlling the size of the update amount in the gradient direction. is the gradient, which is the partial differential with respect to the estimated parameter (reconstructed image). And, the update formula for the j-th pixel is expressed by the following (Formula 3).

[0012] [Formula 3]

[0013]

[0014] In the above (Formula 3), α and β are treated as quantities that do not depend on the number of repetitions and the pixel position, and R is treated as a quantity that does not depend on the number of repetitions. In contrast, they can also be treated as quantities that depend on the number of repetitions and the pixel position. For example, the above-mentioned non-patent document 2 is an image reconstruction method in which α depends on the number of repetitions (and indirectly also depends on the pixel value during reconstruction), and patent document 2 is an image reconstruction method in which α and β depend on the pixel position.

[0015] In this way, when α, β, and R depend on the number of repetitions and the pixel position, the above (Formula 3) can be expressed by the following (Formula 4).

[0016] [Formula 4]

[0017]

[0018] Here, α n , β n , R n Although it is not a direct estimation object, it is an auxiliary variable required to obtain the reconstructed image. It is a variable that changes with the number of repetitions or pixel positions and is used to determine the update conditions required to obtain the reconstructed image. Such a variable is called a state variable in this specification. In addition, the state variable can also be called an update condition variable. Here, R n Strictly speaking it is a function, but in this specification it is included and referred to as a state variable.

[0019] Figure 5 : is a flowchart showing a process of reconstructing an image by a successive approximation image reconstruction method using such state variables.

[0020] When reconstructing an image by the successive approximation image reconstruction method, pre-processing is first performed. In this pre-processing, the reconstructed image μ is performed. 0 and the state variable α 0 , β 0 , R 0Initialization (step S11). At this time, as the initial image, for example, a blank image (an image in which all pixel values ​​are zero) can be used.

[0021] Next, perform repetitive processing. This repetitive processing is a processing step in which the calculation represented by the above (Formula 4) is repeatedly performed. At this time, first perform the forward projection processing (step S12), and then perform the back projection processing (step S13). Then, after performing the image update processing (step S14), perform the update processing of the state variable (step S15). At this time, the second term in (Formula 4) is calculated by the forward projection processing and the back projection processing, and the calculation of the third term and the overall addition calculation on the right are performed by the image update processing. Next, α n , β n , R n Update. This repetitive process is repeated until the convergence condition is satisfied (step S16).

[0022] Then, post-processing is performed. In the post-processing, a reconstructed image satisfying a convergence condition is output (step S17).

[0023] Prior art literature

[0024] Patent Literature

[0025] Patent Document 1: Japanese Patent Application Publication No. 2011-156302

[0026] Patent Document 2: U.S. Patent No. 8,958,660

[0027] Non-patent literature

[0028] Non-patent document 1: C.Lemmens: Suppression of Metal Artifacts in CT Using aReconstruction Procedure That Combines MAP and Projection Completion IEEETransactions on Medical Imaging, Volume: 28Issue: 2 (2009)

[0029] Non-patent literature 2: E. Tanaka: Subset-dependent relaxation in brock-iterative algorithms for image reconstruction in emission tomography, Phys Med Biol 48: 1405-1422 (2003) Summary of the invention

[0030] Technical problem to be solved by the invention When reconstructing an image using the successive approximation method, more processing time is required compared to the conventional filtered back projection. Furthermore, when reconstructing an image using the successive approximation method, at the moment when it is determined that a predetermined constant cutoff criterion is satisfied, or at the moment when the operator confirms the image being reconstructed and determines that the required image quality is obtained, the repeated calculation is terminated and the reconstructed image is output. Here, the cutoff criterion for repeated calculation is often set empirically in consideration of processing time and image quality, but the repeated calculation converges at this moment and there is no guarantee that the final solution will be obtained. Therefore, there are also cases where the image quality of the reconstructed image is insufficient after the calculation for reconstruction is completed and recalculation is required. In particular, it is conceivable that such recalculation is often required in industrial CT devices where the imaging object spans multiple branches.

[0031] When performing such a recalculation, as shown in the above (Formula 3), α and β are set to values ​​that are independent of the number of repetitions and the pixel position, and R is set to a value that is independent of the number of repetitions, that is, without using state variables that depend on the number of repetitions, etc., it is sufficient to read in the reconstructed image of the final output and set it to the initial value, and then reconstruct the image using the successive approximation method again.

[0032] On the other hand, when using state variables that depend on the number of repetitions, etc. as shown in the above (Formula 4), the state variables are discarded when recalculation is performed, so it is necessary to reconstruct the image using the iterative approximation method from the beginning.

[0033] For example, even if an image with 100 repetitions is obtained in the initial image reconstruction process and it is determined that the quality of the reconstructed image is insufficient, if one wants to reconstruct an image with 200 repetitions, it is necessary to perform the calculation again from the 1st repetition. If it is assumed that the probabilistic factor is not included in the reconstruction process, the calculation results from the 1st to the 100th time in the second image reconstruction process will be the same as the calculation results of the initial image reconstruction process, resulting in useless calculations.

[0034] The present invention is made to solve the above-mentioned problems, and its purpose is to provide a successive approximation image reconstruction method, a successive approximation image reconstruction program and a tomography device. When an image is reconstructed using the successive approximation method, the calculation time can be shortened and the reconstruction can be performed efficiently even when the image reconstruction is started again.

[0035] Solutions for solving the above technical problems

[0036] The invention described in technical solution 1 is characterized in that, in a successive approximation image reconstruction method for reconstructing an image using a successive approximation method, a state variable that changes with the number of repetitions or the pixel position (depends on the number of repetitions or the pixel position) for determining an update condition required to obtain the reconstructed image is used, the image is reconstructed by the successive approximation method, and the state variable is stored at the end of the reconstruction of the image. When the reconstruction of the image is started again, the image reconstruction is performed after the aforementioned stored state variable is read in.

[0037] The invention described in claim 2 is the invention described in claim 1, wherein an image is reconstructed by successive approximation using a plurality of state variables, and all or part of the plurality of state variables are stored.

[0038] The invention described in claim 3 is the invention described in claim 2, wherein a gradient descent method or a Newton method is used as an optimization algorithm for reconstruction, and the plurality of state variables include a data term and a penalty term.

[0039] The invention described in claim 4 is a successive approximate image reconstruction program for causing a computer to execute the successive approximate image reconstruction method described in any one of claims 1 to 3.

[0040] The invention described in claim 5 is a tomographic imaging apparatus comprising a computing unit for executing the successive approximate image reconstruction program described in claim 4 .

[0041] Effects of the Invention

[0042] According to the invention described in claim 1 to claim 5, when an image is reconstructed using the successive approximation method, even when the image reconstruction is restarted, the calculation time can be shortened and the reconstruction can be performed efficiently.

[0043] According to the invention described in claim 2 and claim 3, the data amount of the stored state variables can be adjusted to an appropriate amount according to the image quality of the reconstructed image. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a schematic diagram of a tomography apparatus to which the successive approximation image reconstruction method of the present invention is applied.

[0045] Figure 2 3 is a functional block diagram of the image reconstruction unit 20 .

[0046] Figure 3 This is a flowchart showing a process of reconstructing an image using the successive approximate image reconstruction method of the present invention.

[0047] Figure 4This is a conceptual diagram showing a basic concept of the successive approximate image reconstruction method of the present invention.

[0048] Figure 5 : is a flowchart showing a process of reconstructing an image using the successive approximation image reconstruction method. DETAILED DESCRIPTION

[0049] Hereinafter, embodiments of the present invention will be described based on the drawings. Figure 1 This is a schematic diagram of a tomography apparatus to which the successive approximation image reconstruction method of the present invention is applied.

[0050] The tomography apparatus is an apparatus for performing X-ray CT imaging of an imaging object 10, and includes a table 13 that rotates around an axis in a vertical direction while placing the imaging object 10, an X-ray tube 11 that irradiates X-rays toward the imaging object 10 that rotates together with the table 13, and a flat panel detector 12 that detects the X-rays that are irradiated from the X-ray tube 11 and pass through the imaging object 10. The flat panel detector 12 obtains X-ray projection data based on the detected X-rays. In addition, other X-ray detectors such as an image intensifier (II) may be used instead of the flat panel detector 12.

[0051] Figure 2 This is a functional block diagram of the image reconstruction unit 20 that reconstructs an image by the successive approximation method based on the X-ray projection data acquired by the flat panel detector 12 .

[0052] The image reconstruction unit 20 is composed of a computer and constitutes a part of a control unit that controls the entire device. The computer includes: a CPU as a processor that performs logical operations; a ROM that stores action programs required for controlling the device; and a RAM that temporarily stores data during control.

[0053] The image reconstruction unit 20 includes: a forward projection processing unit 21 for performing forward projection processing; a back projection processing unit 22 for performing back projection processing; an image update processing unit 23 for performing image update processing; and a state variable update processing unit 24 for performing state variable update processing. In addition, the image reconstruction unit 20 includes: a program storage unit 25 for storing a successive approximate image reconstruction program for executing the successive approximate image reconstruction method of the present invention in a computer; a reconstructed image storage unit 26 for storing reconstructed images produced successively; and a state variable storage unit 27 for storing state variables produced successively. The image reconstruction unit 20 and Figure 1 The flat panel detector 12 is shown connected.

[0054] Next, the image reconstruction operation of the successive approximation image reconstruction method of the present invention will be described. Figure 31 is a flowchart showing the process of reconstructing an image by the successive approximate image reconstruction method of the present invention. Figure 4 This is a conceptual diagram showing the basic considerations of the successive approximate image reconstruction method of the present invention. In addition, this embodiment uses the gradient descent method as an optimization algorithm for reconstruction, and is an embodiment of the case where the above (Formula 4) is applied. In addition, the Newton method may be used instead of the gradient descent method.

[0055] When the image is reconstructed using the successive approximation method, such as Figure 4 As shown in FIG. 1 , when an image with 100 repetitions is obtained by the initial image reconstruction process, the image quality of the reconstructed image may be insufficient. In such a case, for example, in order to obtain an image with 200 repetitions, it is necessary to perform recalculations from the first repetition. At this time, if it is assumed that no probabilistic factors are included in the reconstruction process, the calculation results from the first to the 100th repetition in the second image reconstruction process need to be recalculated in the same way as the calculation in the initial image reconstruction process, resulting in useless calculations.

[0056] In contrast, in the successive approximate image reconstruction method of the present invention, the following configuration is adopted: when an image repeated 100 times is obtained by the initial image reconstruction process, if the image quality of the reconstructed image is insufficient, when the image reconstruction is started again, the image reconstruction is started again after reading the reconstructed image and state variables at the end of the reconstruction of the image repeated 100 times.

[0057] That is, Figure 3 As shown, when an image is reconstructed by the successive approximation image reconstruction method of the present invention, pre-processing is first performed. In the pre-processing, the number of successive approximation repetitions Ks is first set as a restart condition, and the number of end times Ke is set as a convergence condition (step S1). In addition, the restart condition is uniquely determined by specifying the reconstructed image. In addition, as a convergence condition, for example, the value of an objective function may also be set.

[0058] Next, the reconstructed image and state variables are set. At this time, it is determined whether the reconstruction process is the first time (step S2). And, when the reconstruction process is the first time, that is, when Ks=0, Figure 5 The same pre-processing is performed as shown in the figure, and the reconstructed image μ is performed. 0 , state variable α 0 , β 0 , R 0 Initialization (step S3). At this time, as the initial image, for example, a blank image (an image in which all pixel values ​​are zero) can be used.

[0059] On the other hand, when the reconstruction process is not the first time, that is, when Ks is not 0 and the reconstruction process is started again, Figure 2 The reconstructed image storage unit 26 shown in FIG. 2 reads the Ks-1th reconstructed image μ Ks－1 , and from Figure 2 The state variable storage unit 27 shown in FIG. 1 reads the state variable α of the Ks-1th time. Ks－1 , β Ks－1 , R Ks－1 .

[0060] Then, repeat the process. Figure 5 The same is true for the case of repeated processing shown in the figure, and the calculation represented by the above (Formula 4) is repeatedly performed. That is, the forward projection processing is first performed (step S5), and then the back projection processing is performed (step S6). Then, after the image update processing (step S7), the state variable update processing is performed (step S8). At this time, the second term in (Formula 4) is calculated through the forward projection processing and the back projection processing, and the calculation of the third term and the overall addition calculation on the right are performed through the image update processing. Next, the state variable α is updated. n , β n , R n The repetitive process is repeated until the convergence condition is met, that is, until the number of repetitions Ks reaches the end number Ke (step S9).

[0061] Then, post-processing is performed. In this post-processing, a reconstructed image and state variables that satisfy the convergence condition are output (step S10). Ke Output, to Figure 2 The reconstructed image storage unit 26 shown in FIG. 1 stores the reconstructed image. In addition, after repeated processing, the updated state variable α is output. Ke , β Ke , R Ke , is stored in Figure 2 The state variable storage unit 27 is shown.

[0062] As described above, in the successive approximation image reconstruction method of the present invention, since a structure is adopted in which when the reconstruction of an image is restarted, the reconstruction of the image is restarted after reading in the reconstructed image and state variables at the end of the previous reconstruction. Therefore, when the image is reconstructed using the successive approximation method, even when the reconstruction of the image is restarted, the calculation time can be shortened and the reconstruction can be performed efficiently.

[0063] In addition, in the above-mentioned embodiment, as Figure 2 The state variables stored in the state variable storage unit 27 shown in FIG. Ke , β Ke , R Ke All of it, but αKe , β Ke , R Ke When such an embodiment is adopted, the amount of state variable data that needs to be stored in the state variable storage unit 27 can be adjusted to an appropriate amount according to the image quality of the reconstructed image.

[0064] In addition, in the above-mentioned embodiment, the reconstruction conditions are made the same when the reconstruction process is initially executed and when the reconstruction process is restarted, but, for example, reconstruction may be performed at a low resolution when the reconstruction process is initially executed, and at a high resolution when the reconstruction process is restarted. In addition, a part of the reconstructed image stored in the reconstructed image storage unit 26 or the state variable stored in the state variable storage unit 27 may be changed or created by another method.

[0065] In addition, in the above embodiment, the case where the gradient descent method is used as the optimization algorithm is described, but as mentioned above, the Newton method may be used instead of the gradient descent method, and other optimization algorithms may be used. n , β n , R n , but α can also be used as a state variable n , β n , R n Other state variables.

[0066] Furthermore, in the above-mentioned embodiment, the case where the successive approximate image reconstruction method of the present invention is applied to a tomography apparatus for performing X-ray CT imaging of the imaging object 10 is described, but the successive approximate image reconstruction method of the present invention can also be applied to a medical X-ray CT apparatus or a medical tomosynthesis imaging apparatus, etc.

[0067] Description of Reference Numerals

[0068] 10. Photographic Objects

[0069] 11 X-ray tube

[0070] 12 Flat Panel Detector

[0071] 13 Rotating table

[0072] 20 Image Reconstruction Unit

[0073] 21 Orthographic projection processing unit

[0074] 22 Back projection processing unit

[0075] 23 Image update processing unit

[0076] 24 State variable update processing unit

[0077] 25 Program storage unit

[0078] 26 Reconstruction image storage unit

[0079] 27 State variable storage unit

Claims

1. A successive approximation image reconstruction method, using a successive approximation method to reconstruct an image. in, Reconstructing the first image by a successive approximation method using the first state variable to obtain a first reconstructed image; storing the first state variable and the first reconstructed image when reconstruction of the first image is completed; Before executing reconstruction of the second image, it is determined whether the reconstruction process is the first time. When the reconstruction process is an initial time, initializing the first state variable and the first reconstructed image; When the reconstruction process is not the first time, reading in the first state variable and the first reconstructed image; reconstructing the second image using the second state variable and the first reconstructed image to obtain a second reconstructed image, The first state variable depends on the number of successive approximate repetitions or the pixel position, and is used to determine an update condition for obtaining the first reconstructed image.

2. The successive approximate image reconstruction method according to claim 1, It is characterized in that An image is reconstructed by successive approximation using a plurality of state variables, and all or a portion of the plurality of state variables are stored.

3. The successive approximate image reconstruction method according to claim 2, It is characterized in that A gradient descent method or Newton's method is used as an optimization algorithm for reconstruction, and the plurality of state variables include a data term and a penalty term.

4. A successive approximation image reconstruction procedure, It is characterized in that Used to make a computer execute the successive approximation image reconstruction method according to any one of claims 1 to 3.

5. A tomographic apparatus, It is characterized in that A computing unit for executing the successive approximate image reconstruction program according to claim 4 is provided.

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