Interior CT image reconstruction method, image reconstruction apparatus, and program

Abstract

To perform highly accurate image reconstruction by using easier prescient information in an interior CT.SOLUTION: There is provided an image reconstruction method of an interior CT which reconstructs an image of a region of interest of a cross section of an object by irradiating the region of interest of the object with the X-ray. The image reconstruction method comprises: a projection data acquisition step of acquiring a plurality of pieces of projection data when irradiating the region of interest of the object with the X-ray within a range of a prescribed angle in the peripheral direction of the object; and an image calculation step of obtaining an image of the region of interest by solving Ax=b under prescient information C when a vector in which the plurality of pieces of projection data are arrayed is b, a matrix in which a plurality of projection calculation matrices corresponding to the projection data are arrayed is A and a vector in which image values of the cross section of the object are arrayed is x in a case where the matrix having information on pixels when the X-ray passes through the cross section of the object according to the irradiation angle is the projection calculation matrix. The prescient information C is the total sum of the image values of the image of the cross section of the object.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to an image reconstruction method for generating an image of a physical quantity distribution by measuring the line integral value of a physical quantity distribution inside an object and processing the data, and more particularly to an image reconstruction method for interior CT. [Background technology]

[0002] First, let's explain a CT imaging method called interior CT (Computed Tomography). Generally, in many situations of CT imaging, it is sometimes necessary to obtain images of only a small region of interest (ROI) within an object. For example, in the diagnosis of heart disease or breast cancer using medical CT, images of only a small ROI, including the heart or breast, are sufficient. Current CT system configurations and data acquisition methods, even when images of only the ROI are sufficient, irradiate the cross-section containing the ROI with an X-ray beam that completely covers it, measuring projection data not only of the ROI but also of all straight lines passing through the object's cross-section (see Figure 1(a)). This is because the filtered back-projection (FBP) method, a calculation procedure used for image reconstruction in CT systems, requires projection data of straight lines that do not pass through the ROI in order to generate the ROI image. However, intuitively, projection data of straight lines that do not pass through the ROI is expected to be unnecessary because it does not contain any ROI information. Therefore, an interior CT scanning method involves irradiating only the ROI with X-rays and measuring only the projection data along (all) straight lines passing through the ROI to generate an image of only the ROI (see Figure 1(b)).

[0003] This interior CT offers several advantages compared to conventional CT, which unnecessarily measures projection data. For example, (1) a significant reduction in radiation exposure (sample damage) outside the ROI, (2) a reduction in detector size and X-ray beam width, (3) the ability to image large objects that do not fit within the field of view, and (4) the ability to perform high-resolution CT imaging by irradiating only a small field of view of the object with X-rays and performing magnified imaging.

[0004] On the other hand, in interior CT, projection data on straight lines that do not pass through the ROI is not measured, so a method is needed to reconstruct the image from incomplete projection data with some parts missing. More precisely, the definition of the image reconstruction problem in interior CT described above is as follows: Consider an object f(x,y) and the ROI S that is to be imaged (see Figure 1(b)). Assume that only projection data p(r,θ) (r is the radial vector, θ is the angle) where a straight line passes through the ROI S can be measured. However, for simplicity, we assume that projection data is acquired using parallel beams. In this case, since p(r,θ) where a straight line does not pass through the ROI S is not measured, the projection data for each angle θ will be truncated on the left and right sides and will be missing. The problem of correctly reconstructing the image f(x,y) at the ROI S from such truncated projection data is the image reconstruction of interior CT.

[0005] This problem has been the subject of much research over the years, and is outlined below. First, in Non-Patent Literature 1, Natterer mathematically proved that the solution to interior CT image reconstruction is not "uniquely" determined (where unique means that the solution to image reconstruction is uniquely determined from the projection data, making mathematically correct image reconstruction possible). Because this non-uniqueness was known, many approximate image reconstruction methods have been studied.

[0006] For example, representative methods that have been studied include (1) a method that extrapolates the missing parts on the left and right sides of the projection data in each direction using a smooth function before reconstructing the image, and (2) a method that reconstructs the image using iterative approximation with incomplete projection data. However, these methods have not been put into practical use due to shading artifacts and cupping artifacts caused by approximation errors.

[0007] In response to these previous studies, a mathematically rigorous image reconstruction method was finally discovered in 2007, giving rise to a new direction in image reconstruction for interior CT. The key point of these rigorous solutions can be summarized in one sentence: "While rigorous image reconstruction is impossible with only projection data from interior CT, mathematically rigorous image reconstruction becomes possible with even minimal prior information about the object."

[0008] Regarding the development of the exact solution method described above, first, the 2007 paper by Ye et al. (Non-Patent Literature 2), the 2008 paper by Kudo et al. (Non-Patent Literature 3), and the 2008 patent by Wang et al. (Patent Literature 1) proved that exact image reconstruction of ROI S is possible if prior information is available, such as the image values ​​in an arbitrary sub-region B (prior information region) inside ROI S being known (Method 1).

[0009] Next, the 2009 paper by Yu et al. (Non-Patent Document 4) and the 2014 patent by Wang et al. (Patent Document 2) proved that if the image values ​​across the entire ROI S are piecewise uniform (consisting of a finite number of regions with perfectly constant values), then rigorous image reconstruction of the ROI S is possible (Method 2).

[0010] Furthermore, Kudo et al.'s 2017 patent (Patent Document 3) and Kudo's paper (Non-Patent Document 5) successfully reduced the prior information required in the methods of Yu et al. and Wang et al., proving that if the image values ​​are piecewise uniform (or piecewise polynomial) in any sub-region B (prior information region) within the ROI S, then rigorous image reconstruction of the ROI S is possible. They also proposed a practical method to impose the constraint of piecewise uniformity only on the edges of the ROI S (Method 3).

[0011] Finally, Kudo et al.'s currently pending patent application from 2017 (Patent Document 4) devised an exact solution method for fan-beam CT that utilizes partial complete projection data. Specifically, they proved that exact image reconstruction of ROI S is possible if, in addition to the projection data from interior CT, projection data from a complete scan without truncation within a finite angular range E (which can be very small) is available (Method 4). [Prior art documents] [Patent Documents]

[0012] [Patent Document 1] U.S. Patent No. 7697658 [Patent Document 2] U.S. Patent No. 8811700 [Patent Document 3] Patent No. 6760611 [Patent Document 4] International Publication No. 2018 / 179905 [Non-patent literature]

[0013] [Non-Patent Document 1] Natterer F, “The Mathematics of Computerized Tomography”, Wiley, 1986. [Non-Patent Document 2] Ye Y, Yu H, Wei Y, Wang G, “A general local reconstruction approach based on a truncated Hilbert transform”, International Journal of Biomedical Imaging 2007: Article ID 63634, 2007. [Non-Patent Document 3] Kudo H, Courdurier M, Noo F, Defrise M, “Tiny a priori knowledge solves the interior problem in computed tomography”, Physics in Medicine and Biology 53: 2207-2231, 2008. [Non-Patent Document 4] Yu H, Wang G, “Compressed sensing based interior tomography”, Physics in Medicine and Biology 54: 2791-2805, 2009. [Non-Patent Document 5] Kudo, “Advanced compressed sensing image reconstruction for interior tomography”, Proc. SPIE, 2019. [Overview of the project] [Problems that the invention aims to solve]

[0014] However, as mentioned above, in order to perform image reconstruction without degradation of image quality in interior CT, it is necessary to use some prior information about the object in addition to projection data (Methods 1, 2, and 3), or to measure extra supplemental projection data (Method 4). These methods are quite complex, and in many cases prior information cannot be obtained, or it is difficult to modify the equipment to measure supplemental projection data.

[0015] This invention was made to solve these problems, and aims to provide an image reconstruction method that enables high-precision image reconstruction using simpler prior information in interior CT. [Means for solving the problem]

[0016] A first aspect of the present invention is an image reconstruction method for interior CT, which reconstructs an image of a region of interest in a cross-section of an object by irradiating the region of interest in an object with X-rays, comprising: a projection data acquisition step of acquiring a plurality of projection data when X-rays are irradiated into the region of interest of the object within a predetermined angular range in the circumferential direction of the object; and an image calculation step of solving Ax=b under prior information C to obtain an image of the region of interest, where prior information C is the sum of the image values ​​of the cross-section of the object, with b being a vector formed by arranging the plurality of projection data, A being a matrix formed by arranging the plurality of projection matrix corresponding to the projection data, and x being a vector formed by arranging the image values ​​of the cross-section of the object, and the prior information C is the sum of the image values ​​of the cross-section of the object.

[0017] A second aspect of the present invention is an image reconstruction apparatus for interior CT that irradiates a region of interest of an object with X-rays to reconstruct an image of the region of interest in a cross-section of the object, comprising: a projection data acquisition unit that acquires a plurality of projection data when X-rays are irradiated with the region of interest of the object within a predetermined angular range in the circumferential direction of the object; and an image calculation unit that, when a matrix having pixel information as the X-rays pass through the cross-section of the object according to the irradiation angle is defined as a projection operation matrix, a vector formed by arranging the plurality of projection data is denoted as b, a matrix formed by arranging the plurality of projection operation matrices corresponding to the projection data is denoted as A, and a vector formed by arranging the image values ​​of the cross-section of the object is denoted as x, solves Ax=b under prior information C to obtain an image of the region of interest, wherein the prior information C is the sum of the image values ​​of the cross-section of the object.

[0018] A third aspect of the present invention is a program for causing a computer to function as an interior CT image reconstruction device that irradiates a region of interest of an object with X-rays and reconstructs an image of the region of interest in a cross-section of the object, wherein the computer functions as projection data acquisition means for acquiring a plurality of projection data when X-rays are irradiated with the region of interest of the object within a predetermined angular range in the circumferential direction of the object, and an image calculation means for solving Ax=b under prior information C to obtain an image of the region of interest, where the prior information C is the sum of the image values ​​of the image of the cross-section of the object. [Effects of the Invention]

[0019] According to the present invention, it is possible to provide an image reconstruction method that enables high-precision image reconstruction using simpler prior information in interior CT. [Brief explanation of the drawing]

[0020] [Figure 1] This is a schematic diagram comparing a standard CT scan with an interior CT scan. [Figure 2] This is a schematic diagram showing the overall configuration of X-ray CT scanner 1. [Figure 3] This is a schematic diagram representing projection data. [Figure 4] This figure illustrates the principle of the image reconstruction method in the interior CT according to the first embodiment. [Figure 5] This figure shows an example of obtaining prior information C, which is the sum of image values. [Figure 6] This diagram shows the pixels of an object's cross-section and how X-rays pass through them. [Figure 7] This figure shows an example of a projection matrix A and the measurement equation Ax=b. [Figure 8]This is a schematic block diagram showing an example of the functional configuration of the image reconstruction apparatus 122 according to the first embodiment. [Figure 9] This flowchart shows an example of the processing procedure of the image reconstruction apparatus 122 according to the first embodiment. [Figure 10] This flowchart shows the processing procedure of the ART method, which is an example of an iterative method. [Figure 11] This figure illustrates the principle of the image reconstruction method in the sparse-view interior CT of the second embodiment. [Figure 12] This is a schematic block diagram showing an example of the functional configuration of the image reconstruction apparatus 122A according to the second embodiment. [Figure 13] This flowchart shows an example of the processing procedure of the image reconstruction apparatus 122A according to the second embodiment. [Figure 14] This figure shows the results of a comparative experiment using head CT images, comparing the image reconstruction method of the first embodiment with a conventional image reconstruction method. [Figure 15] This figure shows the results of a comparative experiment using abdominal CT images, comparing the image reconstruction method of the first embodiment with a conventional image reconstruction method. [Figure 16] This figure shows the results of a comparative experiment using polymer blend small piece samples, comparing the image reconstruction method of the second embodiment with the conventional image reconstruction method. [Modes for carrying out the invention]

[0021] Embodiments of the present invention will be described in detail below with reference to the drawings. In this embodiment, the present invention will be described with reference to a medical X-ray CT scanner, but the present invention is applicable to PET (Positron Emission Tomography), SPECT (Single Photon Emission CT), MRI (Magnetic Resonance Imaging), industrial and commercial CT scanners, CT scanners for material measurement, electron beam tomography scanners, etc.

[0022] [X-ray CT device] First, the overall configuration of the X-ray CT apparatus 1 according to the present invention will be described with reference to Figure 2. As shown in Figure 2, the X-ray CT scanner 1 comprises a scan gantry unit 100, a patient table 105, and a control console 120. The scan gantry unit 100 is a device that irradiates the subject with X-rays and detects the X-rays that have passed through the subject. The control console 120 controls each part of the scan gantry unit 100, acquires the transmitted X-ray data measured by the scan gantry unit 100, and generates images. The patient table 105 is a device on which the subject (object) is placed and which moves the subject in and out of the X-ray irradiation range of the scan gantry unit 100.

[0023] The scan gantry unit 100 includes an X-ray source 101, a rotating disk 102, a collimator unit 103, an X-ray detector 106, a data acquisition device 107, a gantry control device 108, a patient bed control device 109, an X-ray control device 110, and a collimator control device 111. The control console 120 includes an input device 121, an image reconstruction device 122, a storage device 123, a system control device 124, and a display device 125.

[0024] An opening 104 is provided in the rotating disk 102 of the scan gantry unit 100, and the X-ray source 101 and the X-ray detector 106 are positioned opposite each other through the opening 104. The subject, placed on the bed 105, is inserted into the opening 104. The rotating disk 102 rotates around the subject by a driving force transmitted from the rotating disk drive device through the drive transmission system. The rotating disk drive device is controlled by the gantry control device 108.

[0025] The X-ray source 101 is controlled by the X-ray control device 110 to irradiate X-rays of a predetermined intensity continuously or intermittently. The X-ray control device 110 controls the X-ray source voltage and X-ray source current applied to or supplied to the X-ray source 101 according to the X-ray source voltage and X-ray source current determined by the system control device 124 on the control console 120.

[0026] A collimator unit 103 is provided at the X-ray irradiation port of the X-ray source 101. The collimator unit 103 includes a collimator, which is a mechanism that limits the irradiation range of X-rays emitted from the X-ray source 101, and an X-ray compensation filter that adjusts the X-ray dose distribution. The operation of the collimator is controlled by a collimator control device 111. The collimator control device 111 is a device that controls the operation of the collimator and controls the irradiation range of the X-rays emitted from the X-ray source 101.

[0027] X-rays emitted from the X-ray source 101, passing through the collimator unit 103 and then through the subject, are incident on the X-ray detector 106.

[0028] The X-ray detector 106 is composed of, for example, a group of X-ray detection elements, each consisting of a scintillator and a photodiode, arranged in a rotational direction (channel direction) with approximately 1000 elements and in the rotational axis direction (slice direction) with approximately 1 to 320 elements. The X-ray detector 106 is positioned to face the X-ray source 101 through the subject. The X-ray detector 106 detects the amount of X-rays irradiated from the X-ray source 101 and transmitted through the subject, and outputs it to the data acquisition device 107.

[0029] The data acquisition device 107 collects the X-ray dose detected by each X-ray detection element of the X-ray detector 106, converts it into digital data, and sequentially outputs it as transmitted X-ray data to the image reconstruction device 122 on the control console 120.

[0030] The image reconstruction device 122 acquires transmitted X-ray data input from the data acquisition device 107, performs preprocessing such as logarithmic transformation and sensitivity correction to create projection data necessary for reconstruction. The image reconstruction device 122 also reconstructs images such as scanograms and tomographic images (reconstructed images) using the projection data. The image reconstruction device 122 may also generate volume data by stacking the tomographic images of each reconstructed slice. The system control device 124 displays the projection data, scanograms, tomographic images, and volume data generated by the image reconstruction device 122 on the display device 125 and stores them in the storage device 123. Details of the image reconstruction device 122 (122A) will be described later.

[0031] The system control device 124 is a device that controls each part of the control console 120 and the scan gantry unit 100. The image reconstruction device 122 and the system control device 124 are computers equipped with a CPU (Central Processing Unit), ROM (Read Only Memory), RAM (Random Access Memory), and the like.

[0032] The storage device 123 is a device that stores data collected by the data acquisition device 107 and image data created by the image reconstruction device 122, and is specifically a data recording device such as a hard disk. In addition to the transmission X-ray data and image data mentioned above, the storage device 123 also stores programs and data necessary to realize the functions of the X-ray CT device 1.

[0033] The display device 125 consists of a display device such as an LCD panel or CRT monitor and a logic circuit for performing display processing in cooperation with the display device, and is connected to the system control device 124. The display device 125 displays the subject image output from the image reconstruction device 122, as well as various information handled by the system control device 124.

[0034] The input device 121 is a device for inputting the subject's name, examination date and time, examination conditions, etc. Specifically, it consists of a pointing device such as a keyboard or mouse, and various switch buttons. The input device 121 outputs various instructions and information entered by the operator to the system control device 124. The operator operates the X-ray CT apparatus 1 interactively using the display device 125 and the input device 121. The input device 121 may also be a touch panel type input device integrated with the display screen of the display device 125.

[0035] [Projection data] Here, projection data will be explained using Figure 3. Figure 3(a) shows projection data in the case of a parallel beam system. Assume that the X-ray source is rotated θ in the rotational direction. Let f(x,y) be the absorption coefficient distribution of the cross section at the target position on the z axis of the object (subject). The X-rays irradiated from the X-ray source are attenuated by integrating with the absorption coefficient distribution f(x,y) of the linear pixels (x,y) that have passed through the cross section, and are detected as transmitted X-ray data at position r on the axis of the X-ray detector. The image reconstruction device 122 performs logarithmic transformation, sensitivity correction, etc. on this transmitted X-ray data to obtain projection data p(r,θ). The same applies to the fan beam configuration shown in Figure 3(b). To obtain complete projection data, the angle range θ is 180 degrees for the parallel beam method and 360 degrees for the fan beam method. Also, the radial movement r is the distance from one end of the object (or region of interest) to the other.

[0036] [First Embodiment] Next, a first embodiment of the present invention will be described. The first embodiment is an image reconstruction method in a normal interior CT scanner. First, the principle of the image reconstruction method in the interior CT scanner of the first embodiment will be explained using Figures 4 to 7. Hereafter, the subject will also be referred to as an object.

[0037] As shown in Figure 4, in the image reconstruction method of this embodiment, an image of the target cross-section of an object is considered, and it is assumed that the region of interest (ROI) S is included within that image. The image is given image values ​​f(x,y) corresponding to the absorption coefficient distribution. Support Ω is the region of existence of the object, which is set to include the object, and the image value is 0 outside of support Ω. In the image reconstruction method of this embodiment, the interior CT irradiates the region of interest S of the object with X-rays from an X-ray source within a predetermined angular range (e.g., 360°) in the rotational direction, and acquires projection data via a detector. For example, several hundred to several thousand projection data points are acquired. As mentioned above, in interior CT, if the image is reconstructed using only projection data, the solution is not uniquely determined.

[0038] Therefore, in the image reconstruction method of this embodiment, the sum of the image values ​​of the cross-section of the object is used as prior information.

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[0039] Prior information C is obtained, for example, as follows: 1. As shown in Figure 5, complete projection data including the entire cross-section of the object is obtained from one direction (one angle in the rotational direction), and the sum of these is defined as prior information C. Since only the sum of image values ​​C is used, the projection data for the region of interest S may be acquired using a different device than the interior CT scanner used to acquire the projection data. Furthermore, the projection data may have a different resolution than the projection data for the region of interest S, or it may be projected in a different position. In addition, the angle may be measured from any direction, and the projection data may be noisy with a low signal-to-noise ratio.

[0040] 2. Prior information C is calculated using equation (1) from images taken at a different time than the time projection data is acquired for the region of interest S using interior CT. Furthermore, since the sum of image values ​​does not change much even for moving objects, in the case of video recording, prior information C can also be calculated using equation (1) from frame images at different times.

[0041] 3. Before imaging with interior CT, a simple image acquisition (pre-scan) is performed under unfavorable conditions (low quality) such as low signal-to-noise ratio, low resolution, and short measurement time, and the sum of image values ​​C is calculated from the reconstructed image f(x,y). Since only the sum of image values ​​C is used, the prescan can be taken with a different device than the interior CT, have different resolutions, be misaligned, or have high noise and a low signal-to-noise ratio. Furthermore, if the subject has little temporal variation, the prescan can be performed at a different time than when the projection data is acquired.

[0042] Thus, compared to the conventional methods (1) to (4) described above, prior information C consists of only one scalar value, making it far less informative and easier to obtain. Furthermore, since prior information C consists only of the total value C (scalar value) of the images, it can be considered to be close to the minimum amount of prior information.

[0043] The image reconstruction method of this embodiment obtains an image (image value) of the region of interest by solving the following simultaneous conditions using an iterative method. First, let x be a vector formed by arranging the image values ​​of the cross-section of the object (each element is x i (Assuming this is the case), the vector formed by arranging the image values ​​inside the region of interest S is x ROI Let x be a vector formed by arranging the image values ​​outside the region of interest in the cross-section of the object. EXT (Note that vector arrow symbols will be omitted in the text.)

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[0044] Based on prior information C, the sum of the image values ​​inside support Ω (inside the object) is C.

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[0045] X-rays are irradiated onto the region of interest S within a predetermined angular range in the rotational direction, and each acquired projection data is represented as a vector. iLet it be so. Also, a matrix having pixel information when X-rays pass through a cross-section of an object according to the irradiation angle is defined as a projection operation matrix (described later), and the projection data b i The projection operation matrix corresponding to is A i Let it be so. Then, the vector b i When the vector arranged in a single column is b, and the matrix arranged in a single column is A, the measurement equation is expressed as in Equation (4). i When the matrix arranged in a single column is A, the measurement equation is expressed as in Equation (4).

Equation

[0046] The image reconstruction method of this embodiment solves the equations (2), (3), and (4) simultaneously by an iterative method to obtain a vector x that is the solution. Among the obtained vectors x, the image (image value) x ROI of the region of interest is reconstructed with high precision. The iterative method used in the image reconstruction method can be any iterative method known in the CT field, such as the ART (Algebraic Reconstruction Technique) method, the SIRT (Simultaneous Iterative Reconstruction Technique) method, the statistical image reconstruction method (Transmission Maximum Likelihood, etc.) (outside the support, the image f(x, y) is 0, and the constraint on the sum C of the image values is modified to be imposed after each iteration). Note that the initial value of the vector x when solving by the iterative method is not particularly limited.

[0047] Here, a simple example of the projection operation matrix A and the measurement equation Ax = b will be described using FIGS. 6 and 7. As shown in FIG. 6(a), there is a support Ω that is the region where the object exists, the object is included therein, and there is a region of interest S in the object. In this case, the pixels of the region of interest S are x1 to x7. Also, the pixels of the object (cross-section) include the region of interest and are x1 to x 21 Therefore, x = [x1, x2, ···, x 21 T and x ROI = [x1, x2, ···, x7] T and x EXT ​=[x8,x9,···,x 21 ] T (T represents transpose).

[0048] As shown in Figure 6(b), consider three X-rays l1, l2, and l3, and assume that the X-rays are irradiated at an angle of 0° with respect to the axis. In this case, X-ray l1 is directed to pixel x 11 ,x 12 x1,x2,x 13 The X-ray passes through, and the integrated value (or a value based on it) of these image values ​​is acquired as projection data. X-ray l2 is used for pixel x 14 x3,x4,x5,x 15 The X-ray passes through, and the integrated value (or a value based on it) of these image values ​​is acquired as projection data. X-ray l3 is used for pixels x 16 x6,x7,x 17 ,x 18 The X-rays pass through, and the integrated value (or a value based on it) of these image values ​​is obtained as projection data. At this time, the information of the pixels (positions) through which the X-rays pass and the pixel information of the object x=[x1,x2,···,x 21 ] T The projection matrix A1 can be determined from this. The projection data at this time is denoted as b1.

[0049] Furthermore, as shown in Figure 6(c), suppose that three X-rays l1, l2, and l3 are irradiated at an angle of 90° to the axis. In this case, X-ray l1 is directed to pixel x 19 x6,x3,x 12 X-ray l2 passes through x8, and the value obtained by integrating these image values ​​(or a value based on it) is acquired as projection data. 20 X-ray l3 passes through x7, x4, x1, x9, and the value obtained by integrating these image values ​​(or a value based on them) is acquired as projection data. X-ray l3 is used for pixel x 21 ,x 17 ,x5,x2,x 10 The X-rays pass through, and the integrated value (or a value based on it) of these image values ​​is obtained as projection data. At this time, the information of the pixels (positions) through which the X-rays pass and the pixel information of the object x=[x1,x2,···,x 21 ] T The projection matrix A2 can be determined from this. The projection data at this time is denoted as b2.

[0050] If there are only two projection data points, b1 and b2, then if we arrange b1 and b2 in a column to form vector b, and arrange the corresponding projection matrices A1 and A2 in a column to form matrix A, the measurement equation Ax=b becomes as shown in Figure 7. In this case, b(b1,b2) on the right-hand side is actually the projection data. Note that although the elements of matrix A in the figure are 1, they are not limited to 1. Also, blank elements in matrix A are 0.

[0051] Figure 8 is a schematic block diagram showing an example of the functional configuration of the image reconstruction apparatus 122 according to the first embodiment. The image reconstruction apparatus 122 comprises a prior information acquisition unit 131, a projection data acquisition unit 132, and an image calculation unit 133. The image reconstruction apparatus 122 may be provided as part of the X-ray CT apparatus 1, as shown in Figure 2, or it may be connected to the X-ray CT apparatus 1 as a separate unit. In addition, the image reconstruction apparatus 122 may operate independently and acquire necessary information from an external server or storage device via a network.

[0052] The prior information acquisition unit 131 acquires the sum of the image values ​​of the cross-sectional image of the object as prior information C. The prior information C is calculated using the following formula.

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[0053] The prior information acquisition unit 131 may acquire complete projection data including the entire cross-section of the object from one direction (one angle in the rotational direction) and calculate the sum of these as prior information C. Alternatively, the prior information acquisition unit 131 may calculate prior information C from a captured image including the object using equation (5). Alternatively, the prior information acquisition unit 131 may calculate prior information C from an image easily pre-scanned under adverse conditions (low quality) using equation (5). Alternatively, the prior information acquisition unit 131 may acquire the value of equation (5) stored in the storage device 123 or the like as prior information C.

[0054] The projection data acquisition unit 132 acquires multiple projection data when X-rays are irradiated onto the region of interest of an object within a predetermined angular range (e.g., 360°) in the circumferential direction of the object. For example, the projection data acquisition unit 132 acquires several hundred to several thousand projection data. The projection data acquisition unit 132 may use projection data acquired while imaging with the X-ray CT device 1, or it may acquire projection data that has been previously stored in the storage device 123.

[0055] The image calculation unit 133, when using a matrix containing pixel information as the X-ray passes through the cross-section of an object according to the irradiation angle as the projection matrix, calculates multiple projection data b i Let b be the vector formed by arranging the data, and let b be the projection data. i Corresponding to multiple projection matrices A i Let A be a matrix formed by arranging the values, and let x be a vector formed by arranging the image values ​​of the cross-section of the object. Under prior information C, we solve Ax=b to obtain the image of the region of interest. Specifically, the image calculation unit 133 sets x to a vector of image values ​​of the cross-section of an object (each element being x i (Assuming this is the case), the vector formed by arranging the image values ​​inside the region of interest S is x ROI Let x be a vector formed by arranging the image values ​​outside the region of interest in the cross-section of the object. EXT Let's assume that.

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[0056] The image calculation unit 133 determines C to be the sum of the image values ​​inside the support Ω (inside the object).

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[0057] The image calculation unit 133 converts each projection data acquired by the projection data acquisition unit 132 into vector b i Projection data b i The projection matrix corresponding to this operation is A i The image calculation unit 133 then calculates vector b i Let b be a vector formed by arranging the elements in a single column, and matrix A i Let A be a matrix formed by arranging the elements in a single column. Then the measurement equation is formulated as shown in equation (4).

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[0058] The image calculation unit 133 solves equations (6), (7), and (8) simultaneously and uses an iterative method to find the solution vector x, and the x within x ROI This will be the image of the region of interest.

[0059] Next, the operation of the image reconstruction apparatus 122 according to the first embodiment will be described with reference to Figures 9 and 10. Figure 9 is a flowchart showing an example of the processing procedure of the image reconstruction apparatus 122 according to the first embodiment. First, the prior information acquisition unit 131 acquires the sum of the image values ​​of the cross-sectional image of the object as prior information C (step S101).

[0060] Next, the projection data acquisition unit 132 acquires projection data b when X-rays are irradiated onto the region of interest of the object within a predetermined angular range in the circumferential direction of the object. i Obtain multiple values ​​(step S102).

[0061] Next, the image calculation unit 133 uses a matrix containing pixel information as the X-rays pass through the cross-section of an object according to the irradiation angle as the projection calculation matrix, and then calculates a plurality of projection data b i Let b be the vector formed by arranging the data, and let b be the projection data. i Corresponding to multiple projection matrices A i Let A be a matrix formed by arranging the values, and let x be a vector formed by arranging the image values ​​of the cross-section of the object. Then we formulate the measurement equation Ax=b (Step S103).

[0062] Next, the image calculation unit 133 solves Ax=b using an iterative method under prior information C, and the solution x ROI This is the image of the region of interest (step S104).

[0063] Figure 10 is a flowchart showing an example of the ART processing procedure, which is an example of the iterative method performed by the image calculation unit 133. The desired image x is obtained as a vector x = (x1, x2, ..., x J ) T Let the projection data be a vector b=(b1,b2,···,b I ) T Let the projection matrix A be the vector a from top to bottom. i T Let (1 ≤ i ≤ I).

[0064] First, the image calculation unit 133 sets the initial value of vector x to x (0) Set as desired (step S201). Next, the image calculation unit 133 performs a predetermined number of main iterations for k (=0,1,2,...) (step S202). Next, the image calculation unit 133 calculates the temporary vector x (k,1) to x (k) Substitute this value (step S203), and perform a sub-iteration for i I times, which is the number of elements in the projected data (step S204).

[0065] Next, the image calculation unit 133 calculates the value b of the projection data. i and the current x (k,i) Vector a in the projection matrix i TA normalized vector a whose coefficients are the difference between the projected value and the resulting value. i The current x (k,i) In addition, the intermediate vector x (k,i+1 / 2) (Step S205)

[0066] Next, the image calculation unit 133 uses prior information C to calculate C (sum of image values) and the intermediate vector x (k,i+1 / 2) The difference between the sum of the image values ​​and the intermediate vector x is divided by the number of pixels in the support Ω. (k,i+1 / 2) In addition to the values ​​of the elements, update vector x (k,i+1) The value of the element is set. However, for pixels not included in the support Ω, the image calculation unit 133 updates the vector x (k,i+1) The value of the element is set to 0. (Step S206).

[0067] Next, the image calculation unit 133, once the sub-iteration is complete, calculates the vector x (k+1) Update vector x (k,I+1) Update (step S207). The image calculation unit 133, once the main iteration is finished, sets the vector x = x (k+1) Having calculated this, the process will be terminated. This concludes the explanation of Figures 9 and 10.

[0068] As explained above, the prior information acquisition unit 131 acquires the sum of image values ​​of the cross-sectional image of the object as prior information C, the projection data acquisition unit 132 acquires multiple projection data when X-rays are irradiated onto the region of interest of the object within a predetermined angular range in the circumferential direction of the object, and the image calculation unit 133 solves Ax=b under the prior information C, where b is the vector of projection data, A is the projection operation matrix, and x is the vector of the image values ​​of the cross-sectional image of the object, to obtain the image of the region of interest.

[0069] As a result, the image reconstruction device 122 can perform high-precision image reconstruction using simpler (ultra-simpler) prior information in interior CT. Furthermore, the prior information C used by the image reconstruction device 122 consists of only one scalar value, making it far less information-intensive and easier to acquire compared to the conventional methods (1) to (4) described above. Therefore, the image reconstruction device 122 is very practical and easy to use. In addition, since the prior information C consists only of the total image value C (scalar value), it is considered to be close to the minimum amount of prior information.

[0070] [Second Embodiment] Next, a second embodiment of the present invention will be described. The second embodiment is an image reconstruction method in sparse-view interior CT. Sparse-view CT is a type of CT that performs imaging by reducing the number of X-ray projection directions. The principle of the image reconstruction method in sparse-view interior CT of the second embodiment will be explained using Figure 11.

[0071] As shown in Figure 11, in the image reconstruction method of this embodiment, we consider an image of the target cross-section of an object, and assume that the region of interest (ROI) S is included within it. The image is given an image value f(x,y) corresponding to the absorption distribution coefficient. Support Ω is the region of existence of the object, which is set to include the object, and the image value is 0 outside of support Ω. In the image reconstruction method of this embodiment, the interior CT irradiates the region of interest S of the object with X-rays from an X-ray source at predetermined intervals within a predetermined angular range (e.g., 360°) in the rotational direction, and acquires projection data via a detector. For example, approximately 80, 64, or 46 projection data points are acquired. As mentioned above, even with sparse-view interior CT, if the image is reconstructed using only projection data, the solution is not uniquely determined, and a high-precision image cannot be obtained.

[0072] Therefore, in the image reconstruction method of this embodiment, the sum of the image values ​​of the cross-section of the object is used as prior information.

number

[0073] The method for acquiring prior information C is the same as that described in the first embodiment. Prior information C is much easier to acquire than the conventional methods (1) to (4) described above, as it consists of only one scalar value, thus providing far less information. Furthermore, since prior information C consists only of the total value C (scalar value) of the image, it is considered to be close to the minimum amount of prior information.

[0074] The image reconstruction method of this embodiment finds a solution by iterating through solving the following conditions simultaneously, and among them, the solution with the smallest TV (Total Variation) norm is obtained as the image (image value) of the region of interest. First, let x be a vector formed by arranging the image values ​​of the cross-section of the object (each element is x i (Assume), vector x ROI and vector x EXT The same definition as in the first embodiment is defined as follows.

number

[0075] Based on prior information C, the sum of the image values ​​inside support Ω (inside the object) is C.

number

number

[0076] X-rays are irradiated onto the region of interest S at predetermined intervals within a predetermined angular range in the rotational direction, and each acquired projection data is represented as a vector. iFurthermore, a matrix containing pixel information as the X-ray passes through the cross-section of the object according to the irradiation angle is used as the projection matrix, and projection data b i The projection matrix corresponding to this operation is A i Let's assume that vector b i Let b be a vector formed by arranging the elements in a single column, and matrix A i When A is a matrix formed by arranging the elements in a single column, the measurement equation can be expressed as shown in equation (4).

number

[0077] The image reconstruction method of this embodiment involves solving equations (9), (10), and (11) simultaneously and finding the solution vector x by an iterative method. However, in the case of sparse-view interior CT, even if a solution that satisfies all three of the above equations simultaneously is found, there are infinitely many solutions, making it impossible to reconstruct a high-precision image. Therefore, the x that minimizes the TV norm expressed by equation (12) is sought.

number

[0078] Figure 12 is a schematic block diagram showing an example of the functional configuration of the image reconstruction device 122A according to the second embodiment. The image reconstruction device 122A comprises a prior information acquisition unit 131, a projection data acquisition unit 132A, and an image calculation unit 133A. The image reconstruction device 122A may be provided as part of the X-ray CT device 1, as shown in Figure 2, or it may be connected to the X-ray CT device 1 as a separate unit. In addition, the image reconstruction device 122A may operate independently and acquire necessary information from an external server or storage device via a network. The prior information acquisition unit 131 is the same as the prior information acquisition unit 131 of the image reconstruction apparatus 122 in the first embodiment, and thus the description thereof is omitted.

[0079] The projection data acquisition unit 132A acquires a plurality of projection data when irradiating the region of interest of an object with X-rays sparsely at a predetermined interval within a predetermined angle range (e.g., 360°) in the circumferential direction of the object. For example, the projection data acquisition unit 132A acquires about 80, 64, or 46 pieces of projection data. Note that the projection data acquisition unit 132A may use the projection data acquired while imaging with the X-ray CT apparatus 1, or may acquire the projection data stored in the storage device 123 in advance.

[0080] When the image calculation unit 133A uses a matrix having pixel information when X-rays pass through a cross-section of an object according to the irradiation angle as a projection calculation matrix, a vector obtained by arranging a plurality of projection data b i is defined as b, a matrix obtained by arranging a plurality of projection calculation matrices A i corresponding to the projection data b i is defined as A, and when a vector obtained by arranging the image values of the cross-section of the object is defined as x, the solution of Ax = b is obtained so that the TV norm is minimized under the prior information C, and an image of the region of interest is obtained. Specifically, the image calculation unit 133A sets a vector obtained by arranging the image values of the cross-section of the object as x (each element is denoted as x i ), and vectors x ROI and x EXT are defined as follows.

Equation

[0081] The image calculation unit 133A sets C as the sum of the image values inside the support Ω (inside the object).

Equation

Equation

[0082] The image calculation unit 133A uses each projection data acquired by the projection data acquisition unit 132 as a vector b i and uses the projection calculation matrix corresponding to the projection data b i as A i Then, the image calculation unit 133A uses the vector obtained by arranging the vector b i in a column as b, and when using the matrix obtained by arranging the matrix A i in a column as A, formulates the measurement equation as shown in Equation (15). [Number]

[0083] The image calculation unit 133A simultaneously solves Equations (13), (14), and (15), and uses an iterative method to[[ID=P25]] obtain a vector x that minimizes the TV norm represented by Equation (16). [Number] Then, the image calculation unit 133A uses the obtained x ROI [[ID=P35]]as the image of the region of interest.

[0084] Next, referring to FIG. 13, the operation of the image reconstruction apparatus 122A according to the second embodiment will be described. FIG. 13 is a flowchart showing an example of the processing procedure of the image reconstruction apparatus 122A according to the second embodiment. First, the prior information acquisition unit 131 acquires the sum of the image values of the image of the cross-section of the object as prior information C (step S301).

[0085] Next, the projection data acquisition unit 132A acquires a plurality of projection data b i corresponding to when irradiating the region of interest of the object with X-rays at a predetermined interval within a predetermined angle range in the circumferential direction of the object (step S302).

[0086] Next, the image calculation unit 133A, when using a matrix containing pixel information as the X-rays pass through the cross-section of an object according to the irradiation angle as the projection matrix, calculates multiple projection data b i Let b be the vector formed by arranging the data, and let b be the projection data. i Corresponding to multiple projection matrices A i Let A be a matrix formed by arranging the values, and let x be a vector formed by arranging the image values ​​of the cross-section of the object. Then we formulate the measurement equation Ax=b (Step S303).

[0087] Next, the image calculation unit 133A uses an iterative method under prior information C to find the solution x of Ax=b such that the TV norm is minimized. The image calculation unit 133A uses, for example, the ART method for the iterative method, and the processing procedure is the same as in Figure 10. Then, the image calculation unit 133A calculates the x of the obtained x ROI This is the image of the region of interest (step S304). This concludes the explanation of Figure 13.

[0088] As explained above, the prior information acquisition unit 131 acquires the sum of image values ​​of the cross-sectional image of the object as prior information C, the projection data acquisition unit 132A acquires multiple projection data when X-rays are irradiated onto the region of interest of the object at predetermined intervals within a predetermined angular range in the circumferential direction of the object, and the image calculation unit 133A, when the vector of projection data is b, the projection operation matrix is ​​A, and the vector of the image values ​​of the cross-sectional image of the object is x, finds the solution x of Ax=b under prior information C such that the TV norm is minimized and takes the image of the region of interest as the image.

[0089] As a result, the image reconstruction device 122A can perform high-precision image reconstruction using simpler (ultra-simpler) prior information in sparse-view interior CT. In particular, it can perform high-precision image reconstruction even in sparse-view interior CT, which is more difficult than conventional interior CT. Furthermore, the prior information C used by the image reconstruction device 122A consists of only one scalar value, making it far less information-intensive and easier to acquire compared to the conventional methods (1) to (4) described above. Therefore, the image reconstruction device 122A is very practical and easy to use. In addition, since the prior information C consists only of the total image value C (scalar value), it is considered to be close to the minimum amount of prior information.

[0090] [Example of reconstruction based on simulation experiment of the first embodiment] Next, we will show an example of reconstruction obtained from a simulation experiment performed using the image reconstruction apparatus 122 (image reconstruction method) of the first embodiment.

[0091] Figure 14 shows the results of image reconstruction using simulation experiments on head CT images. Except for (d), the display range for image density is [-20HU, 90HU] (unit: HU: Hounsfield Unit).

[0092] Figure 14(a) is an image reconstructed from complete projection data in a conventional CT scan (not an interior CT scan) using a filtered back projection method. Figure 14(b) is an image reconstructed from projection data of an interior CT scan using the conventional method (3) (using prior information that the ROI boundary is segmentally uniform). Figure 14(c) is an image reconstructed from projection data of an interior CT scan using the conventional method (4) (using prior information that complete projection data in one direction is uniform).

[0093] Figure 14(d) shows an image reconstructed from IntelliCT projection data using the image reconstruction method of Embodiment 1, but without using prior information C, which is the sum of image values. In this case, the area around the ROI boundary is not accurately reconstructed, and the image density is also shifted to [90HU, 200HU]. On the other hand, Figure 14(e) shows an image reconstructed from IntelliCT projection data using the image reconstruction method of Embodiment 1, but with prior information C, which is the sum of image values. In this case, it can be seen that the inside of the ROI is reconstructed at a level comparable to that of Figures 14(a), (b), and (c).

[0094] Figure 15 shows the results of image reconstruction using a simulation experiment on abdominal CT images. Except for (d), the display range of image density is [-100HU, 300HU]. The experiment in Figure 15 is for cases where image reconstruction is difficult due to a small ROS in the region of interest.

[0095] Figure 15(a) is an image reconstructed from complete projection data in a conventional CT scan (not an interior CT scan) using a filtered back projection method. Figure 15(b) is an image reconstructed from projection data of an interior CT scan using the conventional method (3). Figure 15(c) is an image reconstructed from projection data of an interior CT scan using the conventional method (4).

[0096] Figure 15(d) shows an image reconstructed from IntelliCT projection data using the image reconstruction method of Embodiment 1, but without using prior information C, which is the sum of image values. In this case, the area around the ROI boundary is not accurately reconstructed, and the image density is also shifted to [310HU, 710HU]. On the other hand, Figure 15(e) shows an image reconstructed from IntelliCT projection data using the image reconstruction method of Embodiment 1, but with prior information C, which is the sum of image values. In this case, it can be seen that the inside of the ROI is reconstructed at a level comparable to that of Figures 15(a), (b), and (c).

[0097] [Example of reconstruction based on simulation experiment of the second embodiment] Next, we will show an example of reconstruction obtained from a simulation experiment performed using the image reconstruction apparatus 122A (image reconstruction method) of the second embodiment. Figure 16 shows the results based on actual data obtained by measuring polymer blend small pieces using X-ray phase CT.

[0098] Figure 16(a) shows an image reconstructed using a filtered back projection method from complete projection data in 522 directions in a normal sparse-view CT (not an interior CT). Figure 16(b) shows an image reconstructed using the image reconstruction method of Embodiment 2 from projection data in 46 directions of a sparse-view interior CT, but without using prior information C of the sum of image values. In this case, the values ​​are significantly shifted, and the entire image is black. On the other hand, Figure 16(c) shows an image reconstructed using the image reconstruction method of Embodiment 2 from projection data in 46 directions of a sparse-view interior CT, but using prior information C of the sum of image values. In this case, it can be seen that the inside of the ROI can be reconstructed at a level similar to that of Figure 16(a).

[0099] Although embodiments of the present invention have been described in detail above with reference to the drawings, the specific configuration is not limited to these embodiments, and design changes and the like are also included within the scope of the gist of the present invention. [Industrial applicability]

[0100] Embodiments of the present invention are applicable to medical X-ray CT scanners, non-destructive testing CT scanners, material measurement CT scanners, electron beam tomography scanners, and the like. [Explanation of symbols]

[0101] 1 X-ray CT device 100 Scan Gunner Unit 101 X-ray source 102 Rotating discs 103 Collimator Unit 104 Opening 105 berths 106 X-ray detector 107 Data acquisition device 120 Control console 121 Input device 122, 122A Image reconstruction device 123 Storage device 124 System Control Unit 125 Display device 131 A priori information acquisition department 132, 132A Projection data acquisition unit 133, 133A Image calculation unit

Claims

1. An interior CT image reconstruction method for reconstructing an image of a region of interest in a cross-section of an object by irradiating the region of interest of the object with X-rays, A projection data acquisition step of acquiring multiple projection data when X-rays are irradiated onto the region of interest of the object within a predetermined angular range in the circumferential direction of the object, When a projection matrix is ​​defined as a matrix whose elements contain information about the length through which the X-ray passes at each pixel included in the cross-section of the object, and when a vector of multiple projection data is denoted as b, a matrix of multiple projection matrices corresponding to the projection data is denoted as A, and a vector of image values ​​of the cross-section of the object is denoted as x, the image calculation step includes solving Ax = b under prior information C to obtain an image of the region of interest, The prior information C is an image reconstruction method in which the sum of image values ​​of the cross-sectional image of the object is used.

2. In the vector x, the image value outside the object is 0. The image reconstruction method according to claim 1.

3. The aforementioned image calculation step solves Ax = b using an iterative method. The image reconstruction method according to claim 1.

4. The image reconstruction method according to claim 3, wherein, in the iterative method, the vector x is corrected using the prior information C at each iteration.

5. The prior information C is the sum of projection data of the cross-section of the object at one angle in the circumferential direction. The image reconstruction method according to claim 1.

6. The aforementioned prior information C is the sum of image values ​​obtained from an image reconstructed by performing a prescan before capturing the projection data. The image reconstruction method according to claim 1.

7. The projection data acquisition step involves acquiring multiple projection data at predetermined intervals within the predetermined angle range, The image calculation step involves determining the solution x of Ax = b under the prior information C such that a predetermined norm is minimized, thereby obtaining an image of the region of interest. The image reconstruction method according to claim 1.

8. An interior CT image reconstruction apparatus that irradiates a region of interest of an object with X-rays to reconstruct an image of the region of interest in a cross-section of the object, A projection data acquisition unit acquires multiple projection data when X-rays are irradiated onto the region of interest of the object within a predetermined angular range in the circumferential direction of the object. When a projection matrix is ​​defined as a matrix whose elements contain information about the length through which the X-ray passes at each pixel included in the cross-section of the object, and when a vector of multiple projection data is arranged in a row b, a matrix of multiple projection matrices corresponding to the projection data is arranged in a row A, and a vector of image values ​​of the cross-section of the object is arranged in a row x, the image calculation unit solves Ax = b under prior information C to obtain an image of the region of interest, and The prior information C is an image reconstruction device in which the sum of image values ​​of the cross-sectional image of the object is obtained.

9. A program for causing a computer to function as an interior CT image reconstruction device that irradiates a region of interest of an object with X-rays and reconstructs an image of the region of interest in a cross-section of the object, wherein the computer is configured to function as an interior CT image reconstruction device. A projection data acquisition means for acquiring multiple projection data when X-rays are irradiated onto the region of interest of the object within a predetermined angular range in the circumferential direction of the object. When a projection matrix is ​​defined as a matrix whose elements include information on the length through which the X-ray passes at each pixel in the cross-section of the object, and when a vector of multiple projection data is denoted as b, a matrix of multiple projection matrices corresponding to the projection data is denoted as A, and a vector of image values ​​of the cross-section of the object is denoted as x, then the image calculation means functions to obtain an image of the region of interest by solving Ax = b under prior information C. The prior information C is a program that is the sum of the image values ​​of the cross-sectional image of the object.

Images