Method for generating correction filter

Abstract

To provide a method for generating a correction filter suitable for CT reconstruction with a non-circular imaging trajectory.SOLUTION: Provided is a method for generating a correction filter comprising the steps of: setting a virtual point in a virtual space; generating a projection image by projecting the virtual point for each of different imaging positions on an imaging trajectory in the virtual space; generating reconstructed 3D data on the basis of the projection image in the virtual space; generating a reprojection image for each imaging position by projecting the reconstructed 3D data as a subject in the virtual space; performing first Fourier transformation on the projection image; performing second Fourier transformation on the reprojection image; and calculating a correction value for each imaging position on the basis of the projection image after the first Fourier transformation and the reprojection image after the second Fourier transformation.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present disclosure relates to a method for generating a correction filter. [Background technology]

[0002] CT (Computed Tomography) devices that use an X-ray source and an X-ray detector to generate cross-sectional images of a human body or the like are known (see, for example, Patent Document 1).

[0003] When reconstructing 3D data using the Filtered Back Projection (FBP) method in a CT scanner, it is necessary to apply corrections to the projection image (X-ray image) to remove blurring (low-frequency noise) in the reconstructed image. In a typical CT scanner, the imaging trajectory of the X-ray source and X-ray detector is circular, so the necessary correction filter can be theoretically calculated. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2005-021675 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, in CT devices with a free trajectory (irregular trajectory), situations occur where the imaging trajectory of the X-ray source and X-ray detector is not circular in order to avoid robot errors and interference with the subject. When the imaging trajectory is free (irregular trajectory) like this, the noise that appears in the reconstruction has an irregular shape, and there is a problem that it is not possible to calculate the optimal correction filter using a method similar to the FBP method.

[0006] The present disclosure has been made to solve such problems, and provides a method for generating a correction filter suitable for CT reconstruction in which the imaging trajectory is a free trajectory. [Means for solving the problem]

[0007] A method for generating a correction filter according to the present disclosure is a method for generating a correction filter used when reconstructing a three-dimensional X-ray CT image, and includes the steps of: setting a virtual point in a virtual space; generating, in the virtual space, projection images by projecting the virtual point at each of different imaging positions on an imaging orbit; generating, in the virtual space, reconstructed 3D data based on the projection images; generating, in the virtual space, reprojected images by projecting the reconstructed 3D data, which is a subject, at each of the imaging positions; performing a first Fourier transform on the projection images; performing a second Fourier transform on the reprojected images; calculating a correction value for each of the imaging positions based on the projection image after the first Fourier transform and the reprojected image after the second Fourier transform; and storing the imaging positions and the correction values ​​in correspondence with each other.

[0008] With this configuration, it is possible to provide a method for generating a correction filter suitable for CT reconstruction in which the imaging trajectory is a free trajectory.

[0009] In the above-mentioned method for generating a correction filter, the first Fourier transform is performed using the following formula: TIFF2025086273000002.tif20110 The second Fourier transform is performed using the following formula: TIFF2025086273000003.tif21113 The calculation of the correction value is performed using the following formula: TIFF2025086273000004.tif1557 In each of the above equations, the variables x and y may correspond to the coordinates of the projected image or the reprojected image, the variable θ may correspond to the imaging attitude, the variables u and v may correspond to the frequency components after Fourier transform, the function p(x, y, θ) may correspond to the projected image, and the function P(u, v, θ) may correspond to the reprojected image. Effect of the Invention

[0010] According to the present disclosure, it is possible to provide a method for generating a correction filter suitable for CT reconstruction in which the imaging trajectory is a free trajectory. [Brief description of the drawings]

[0011] [Figure 1] 1 is a configuration diagram of a CT apparatus 100 in which a method for generating a correction filter according to an embodiment is implemented. [Diagram 2] FIG. 13A is a flow diagram for calculating a correction value, and FIG. 13B is a flow diagram for correcting a projected image of an actually captured subject. [Diagram 3] 4(a) to 4(c) are conceptual diagrams of the correction value calculation means 4. [Figure 4] (a) Conceptual diagram of relative coordinates, (b) conceptual diagram of relative angles, and (c) conceptual diagram of conversion between two-dimensional coordinates and three-dimensional coordinates. [Diagram 5] 1A is an example of an imaging section 10A which is a first modified example of the imaging section 10, and FIG. 1B is an example of an imaging section 10B which is a second modified example of the imaging section 10. FIG. [Figure 6] 1A is an example of an imaging section 10C which is a third modified example of the imaging section 10; FIG. 1B is an example of an imaging section 10D which is a fourth modified example of the imaging section 10; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Hereinafter, a method for generating a correction filter according to an embodiment of the present invention will be described with reference to the accompanying drawings. In each drawing, corresponding components are given the same reference numerals, and duplicated explanations will be omitted.

[0013] FIG. 1 is a configuration diagram of a CT apparatus 100 (X-ray CT apparatus) in which a method for generating a correction filter according to an embodiment is implemented.

[0014] 1, the CT device 100 includes a correction value creation unit 1 that creates an X-ray projection image correction value 5 (hereinafter also referred to as the correction value 5) and a subject imaging unit 2 that images a subject 40. The CT device 100 may be a cone beam CT device or another CT device such as a helical CT device. The correction value creation unit 1 may be built into the CT device 100 or may be provided outside the CT device 100.

[0015] The correction value creation unit 1 includes an X-ray projection image correction value calculation means 4 (hereinafter also referred to as the correction value calculation means 4) and a correction value recording means 6. The correction value calculation means 4 and the correction value recording means 6 are realized, for example, by a processor executing a predetermined program read from a storage unit (e.g., ROM) to a memory (e.g., RAM). A part or all of these may be realized by hardware. The processor, storage unit, and memory may be built into the CT device 100, or may be provided outside the CT device 100.

[0016] The correction value calculation means 4 calculates the correction value 5 based on the imaging position information 3 at the time of capturing the projection image, i.e., the actual position information of the X-ray source 11 and the X-ray detector 12 at the time the projection image is captured. The process performed by the correction value calculation means 4 will be described later.

[0017] The correction value recording means 6 records the correction value 5 calculated by the correction value calculation means 4 in a storage device (not shown). The storage device may be built in the CT device 100 or may be provided outside the CT device 100.

[0018] The subject photographing section 2 includes an imaging section 10, a control and calculation section 20, and a display device 30.

[0019] The imaging unit 10 places a subject 40 on a rotating table 15, which is a rotating means, and obtains an X-ray projection image.

[0020] The imaging unit 10 includes an X-ray source 11 , a first gripping device 13 , an X-ray detector 12 , a second gripping device 14 , and a rotating table 15 .

[0021] The X-ray source 11 irradiates a subject 40 placed on a rotating table 15 with X-rays.

[0022] The first gripping device 13 grips the X-ray source 11 and adjusts the position of the gripped X-ray source 11 within the imaging system (imaging unit 10). As the first gripping device 13, for example, a robot (industrial robot) having multiple joints may be used.

[0023] The X-ray detector 12 detects the X-rays transmitted through the subject 40. Then, the X-ray detector 12 outputs a projection image (X-ray projection image) of the subject 40, which is X-ray projection image data. The projection image is input to the control and calculation unit 20.

[0024] X-ray detector 12 may have any configuration as long as it can obtain a two-dimensional image of subject 40 as a projected image. For example, X-ray detector 12 may be a flat panel detector that obtains a two-dimensional image of subject 40 as a projected image, or may be a combination of an image intensifier that converts an X-ray transmission image into a visible light image and a visible light sensor such as a CMOS sensor, or may be an X-ray line sensor that obtains a one-dimensional image.

[0025] The second gripping device 14 grips the X-ray detector 12 and adjusts the position of the gripped X-ray detector 12 in the imaging system (imaging unit 10) so that the detector 12 is disposed at a position facing the X-ray source 11. As the second gripping device 14, for example, a robot (industrial robot) having multiple joints may be used.

[0026] The turntable 15 rotates around the central axis of rotation 16 with the subject 40 placed thereon. As a result, the X-ray source 11 and the X-ray detector 12 move relative to the subject 40, so that images of the subject 40 can be captured from multiple directions and projection images of the captured subject 40 can be obtained.

[0027] The control and calculation unit 20 controls each element of the imaging unit 10, creates a correction value 5 for the projection image, corrects the obtained projection image, and reconstructs 3D data based on the corrected projection image.

[0028] The control and calculation unit 20 includes an imaging unit control means 21, an image collecting means 22, an X-ray projection image correction means 24, a 3D data reconstruction means 25, and an image display means 26. The imaging unit control means 21, the image collecting means 22, the X-ray projection image correction means 24, the 3D data reconstruction means 25, and the image display means 26 are realized, for example, by a processor executing a predetermined program (not shown) read from a storage unit (for example, a ROM) to a memory (for example, a RAM). A part or all of these may be realized by hardware. The processor, storage unit, and memory may be the same as the processor, storage unit, and memory that realize the X-ray projection image correction value calculation means 4 and the correction value recording means 6, or may be different processor, storage unit, and memory.

[0029] The imaging unit control means 21 controls each element of the imaging unit 10. The imaging unit control means 21 includes a first gripping device control means 211, an X-ray irradiation control means 212, a rotating table control means 213, a detector control means 214, and a second gripping device control means 215.

[0030] The first gripping device control means 211 controls the attitude of the first gripping device 13 which grips the X-ray source 11. The X-ray irradiation control means 212 controls the X-ray source 11 (X-ray output conditions and ON / OFF, etc.). The rotating table control means 213 controls the rotating table 15 on which the subject 40 or a calibration jig (not shown) is placed to rotate (360-degree rotation) about the central axis of rotation 16. The detector control means 214 controls the acquisition conditions of a projection image by the X-ray detector 12. The second gripping device control means 215 controls the attitude of the second gripping device 14 which grips the X-ray detector 12.

[0031] The image collecting means 22 collects the projection images output from the X-ray detector 12 and saves (stores) them in a storage device (not shown). The X-ray projection image correcting means 24 corrects the projection images collected by the image collecting means 22 and stored in a storage device (not shown) based on the correction values ​​5 for each projection image (imaging position) obtained by the correction value creating unit 1 and stored (recorded) in the storage device (not shown). The 3D data reconstructing means 25 reconstructs the projection images corrected by the X-ray projection image correcting means 24 into 3D data based on the imaging position information 3 (imaging position information of the X-ray source 11 and the X-ray detector 12, etc.) when the projection images were captured. The image displaying means 26 displays the reconstructed 3D data (three-dimensional image) on the display device 30.

[0032] The display device 30 is a display device such as a liquid crystal display, and displays the 3D data (three-dimensional image) reconstructed as described above.

[0033] The method for generating a correction filter according to the present embodiment is a method for generating a correction filter used when reconstructing a three-dimensional X-ray CT image, that is, a correction filter suitable for CT reconstruction on an imaging trajectory from the position information of the X-ray source 11 and the X-ray detector 12 measured in advance. This process is performed analytically, so it does not require repeated calculations. Therefore, this method for generating a correction filter can be realized with low-cost equipment.

[0034] When reconstructing 3D data using the FBP method in a CT scanner, it is necessary to apply corrections to the projection images to remove blurring (low-frequency noise) in the reconstructed image. In a typical CT scanner, the imaging trajectory of the X-ray source and X-ray detector is circular, so the necessary correction filters can be theoretically calculated.

[0035] 1, however, in order to avoid errors in the robots (the first gripping device 13, the second gripping device 14, etc.) and interference with the subject 40, the imaging trajectory of the X-ray source 11 and the X-ray detector 12 may not be circular. When the imaging trajectory is a free trajectory (irregular trajectory) like this, the noise that appears due to reconstruction has an irregular shape, and an optimal correction filter cannot be calculated by a method similar to the FBP method.

[0036] There is a method called iterative approximation that does not require a correction filter, but the calculation cost is very high because it requires repeated feedback to obtain an approximation value. Therefore, a large-scale computer or a huge amount of calculation time is required, which is an issue for practical use.

[0037] Next, the process of the correction value calculation means 4 will be described with reference to Fig. 2(a). The correction value calculation means 4 calculates a correction value for the projection images obtained in each imaging direction from the actual positions of the X-ray source 11 and the X-ray detector 12 at the time of imaging.

[0038] FIG. 2(a) is a flow diagram for calculating the correction value, which is carried out by the correction value calculation means 4 in a virtual space (three-dimensional space).

[0039] As a premise, imaging operation data of each of the first gripping device 13 and the second gripping device 14 is created in advance, and imaging position information 3 is obtained, which is information on the relative position (relative coordinates; see FIG. 4(a)) and relative angle (see FIG. 4(b)) of the X-ray source 11 and the X-ray detector 12 with respect to the subject 40 in each imaging posture. FIG. 4(a) is a conceptual diagram of the relative coordinates, and FIG. 4(b) is a conceptual diagram of the relative angle. The imaging operation data is data that defines the imaging trajectory. The imaging operation data includes information on the angle of the axis (joint) of the robot, the imaging signal to the X-ray detector 12, and the interlock signal between the robots (imaging has been completed, so it is OK to move to the next posture, movement has been completed, so it is OK to image, etc.). The imaging operation data is used, for example, when the correction value calculation means 4 executes each process of steps S10, S11, and S12 described later. The imaging operation data is also used, for example, when the 3D data reconstruction means 25 creates (reconstructs) 3D data from the projection image (corrected image 67) after step S24 described later. In either case, conversion between two-dimensional coordinates and three-dimensional coordinates is performed (see FIG. 4(c)). This conversion itself can be performed using a known technique provided by, for example, OpenCV (Intel). FIG. 4(c) is a conceptual diagram of conversion between two-dimensional coordinates and three-dimensional coordinates.

[0040] First, a projection image 62 of a virtual point 61 is generated based on the imaging position information 3 (step S10). That is, as shown in FIG. 3(a), a projection image 62 is generated by projecting the virtual point 61 for each of different imaging positions (for example, imaging positions P1 to P5) on a predetermined imaging trajectory 68. Specifically, a virtual point 61, which is a point virtually set in a virtual space, is projected to generate a plurality of projection images 62. At this time, the relative positions of real devices (X-ray source 11, X-ray detector 12, etc.) are reproduced in the virtual space based on the imaging position information 3 and projected.

[0041] 3(a) to 3(c) are conceptual diagrams of the correction value calculation means 4. FIG. 3(a) to 3(c) show slice displays of one cross section of the virtual space. FIG. 3(a) shows the concept of step S10. Reference numeral 61 in FIG. 3(a) shows a virtual point set in the virtual space. Reference numeral 68 in FIG. 3(a) shows an imaging trajectory (free trajectory) during imaging. In a general FBP method, the periphery of the subject is imaged in a circular trajectory. On the other hand, in this embodiment, a circular trajectory with a missing part or a free trajectory (irregular trajectory) where the imaging trajectory is not circular may be considered. Reference numeral 62 in FIG. 3(a) shows projected images imaged at positions P1 to P5 along the imaging trajectory 68.

[0042] Next, reconstructed 3D data 63 is generated from the projection image 62 (step S11). That is, in a virtual space, reconstructed 3D data 63 (see FIG. 3(b)) is generated based on the projection image 62 generated in step S10. Specifically, the projection image 62 captured in step S10 is back-projected to generate the reconstructed 3D data 63. When the imaging trajectory is a perfect circle, blurring occurs around the reconstructed image (3D data), with the brightness decreasing in inverse proportion to the distance from the image. In the FBP method, since the blurring is uniform, a Ram-Lak filter or the like is used as a reconstruction filter to correct the blurring. On the other hand, as shown in FIG. 3(a), when the imaging trajectory is a free trajectory (irregular trajectory) that is not circular, the form of the blurring is not uniform like the reconstructed 3D data 63, so a filter similar to the FBP method cannot perform sufficient correction.

[0043] If a correction filter can be generated that corrects the reconstructed 3D data 63 (three-dimensional image) to the original data, that is, the virtual point 61, then this correction filter can be used to correct blurring and noise in a projected image captured of an actual subject 40 along the same imaging trajectory 68.

[0044] In this embodiment, in order to remove this blur, a correction filter is generated by executing steps S12 and S13.

[0045] First, a reprojection image 64 is generated from the reconstructed 3D data 63 (step S12). That is, as shown in FIG. 3(b), reprojection of the reconstructed 3D data 63 generated in step S11 is performed to generate a plurality of reprojection images 64. At this time, the relative positions of the reconstructed 3D data 63, which is the subject, the X-ray source, and the X-ray detector are determined based on the imaging position information 3. As a result, the projection images 62 (plural) and the reprojection images 64 (plural) have the same imaging attitude at each position along the imaging trajectory 68 (for example, each of the positions P1 to P5), but are projection images that differ from each other in the presence or absence of image blurring due to reconstruction.

[0046] Next, the projection image 62 and the reprojection image 64 are subjected to a Fourier transform, and a correction value 5 (amount of correction) is calculated based on the ratio in frequency space (step S13).

[0047] Since the projection image 62 is a discrete value, the Fourier transform for the projection image 62 is performed using the following discrete Fourier transform equation. Here, x, y are the coordinates of the projection image 62, θ is the imaging attitude, u, v are the frequency components after the Fourier transform, the function p(x, y, θ) corresponds to the projection image 62, and the function P(u, v, θ) corresponds to the projection image 62 after the Fourier transform. N represents the total number of projection images (projection images 62). Note that θ does not represent an angle but represents the "θth projection image (projection image 62) captured." In other words, the θ=1st projection image represents a projection image captured at the imaging position P1, the θ=2nd projection image represents a projection image captured at the imaging position P2, and so on (similarly below), as shown in "Example of recorded correction values" in FIG. 1. Note that the imaging positions (for example, positions P1 to P5) are configured by the information in FIG. 4(a) and FIG. 4(b).

number

[0048]

number

[0049]

number

[0050] Next, the processing of the X-ray projection image correcting means 24 will be described with reference to FIG.

[0051] FIG. 2(b) is a flow diagram for correcting the projection image of the subject 40 that has actually been captured. This correction is performed by the X-ray projection image correcting means 24. The following process may be performed each time a projection image 66 (one image) of the subject 40 is captured at a predetermined posture (the posture of the first gripping device 13 and the second gripping device 14) using the X-ray source 11 and the X-ray detector 12, etc. at each position (for example, positions P1 to P5) along the imaging trajectory 68. Alternatively, the following process may be performed each time a projection image 66 (multiple images) of the subject 40 captured at a predetermined posture (the posture of the first gripping device 13 and the second gripping device 14) at each position (for example, positions P1 to P5) along the imaging trajectory 68 is stored in a storage device (not shown) and a projection image 66 (one image) is read out from the storage device.

[0052] First, as described above, each time a projection image 66 is captured (or each time a projection image 66 is read out), the correction value 5 corresponding to that projection image 66 and its imaging position is called out (step S20). That is, the correction value 5 generated in the same imaging posture as that in which the projection image of the subject 40 was obtained is read out from a storage device (not shown).

[0053] Next, a Fourier transform is performed on the projection image 66 (step S21). The Fourier transform on the projection image 66 is performed using the following equation, where function q(x, y, θ) corresponds to the projection image 66, and function Q(u, v, θ) corresponds to the projection image 66 after the Fourier transform. N represents the total number of projection images (projection images 66) captured.

[0054]

number

[0055] The product of the projection image 66 and the correction value 5 is calculated using the following formula:

[0056]

number

[0057]

number

[0058] As described above, according to this embodiment, it is possible to provide a method for generating a correction filter 5 suitable for CT reconstruction in which the imaging trajectory is a free trajectory.

[0059] Furthermore, according to this embodiment, it is possible to generate and reconstruct an appropriate reconstruction filter in a free orbit imaging posture, and clear data can be obtained.

[0060] Next, a modified example will be described.

[0061] <Variation 1> First, an imaging section 10A which is a first modified example of the imaging section 10 will be described.

[0062] FIG. 5A shows an example of an imaging section 10A which is a first modified example of the imaging section 10. In FIG.

[0063] The imaging unit 10A differs from the imaging unit 10 of the above embodiment in that the rotary table 15 is fixed and that the first gripping device 13 and the second gripping device 14 are rotated synchronously. Other than that, the configuration is the same as that of the above embodiment.

[0064] According to variant example 1, the movable range of the first holding device 13 and the second holding device 14 may restrict the rotation angle of the imaging to less than 360 degrees, reducing the amount of data during reconstruction; however, it is possible to image a larger subject 40 that cannot be rotated using the imaging unit 10 of the above embodiment.

[0065] <Variation 2> Next, an imaging section 10B which is a second modified example of the imaging section 10 will be described.

[0066] FIG. 5B shows an example of an imaging section 10B which is a second modified example of the imaging section 10. In FIG.

[0067] The imaging unit 10B differs from the imaging unit 10 of the above embodiment in that the X-ray source 11 and the X-ray detector 12 are attached to a bracket 17, the first gripping device 13 grips the bracket 17, and the second gripping device 14 is omitted. Other than that, the configuration is the same as that of the above embodiment.

[0068] According to the second modification, it is easier to adjust the relative positions of the subject 40, the X-ray source 11, and the X-ray detector 12 compared to the CT device of the above embodiment, and the burden of adjustment labor of the imaging system, etc. is reduced when imaging only a portion of the subject 40 at multiple locations.

[0069] <Modification 3> Next, an imaging section 10C which is a third modified example of the imaging section 10 will be described.

[0070] FIG. 6A shows an example of an imaging section 10C which is a third modified example of the imaging section 10. As shown in FIG.

[0071] The imaging unit 10C differs from the imaging unit 10 of the above embodiment in that the X-ray source 11 and the X-ray detector 12 are attached to a bracket 17, the first gripping device 13 grips the bracket 17, the second gripping device 14 grips the subject 40 so as to be rotatable about the rotation center axis 16, and the rotating table 15 is omitted. Other than that, the configuration is the same as that of the above embodiment.

[0072] According to variant example 3, by using the second holding device 14 as a rotating table 15, for example by adding an automatic picking function, which is an existing technology, to the second holding device 14, it becomes possible to automate X-ray CT imaging of a large number of subjects 40.

[0073] <Variation 4> Next, an imaging section 10D which is a fourth modified example of the imaging section 10 will be described.

[0074] FIG. 6B shows an example of an imaging section 10D which is a fourth modified example of the imaging section 10. In FIG.

[0075] The imaging unit 10D differs from the imaging unit 10 of the above embodiment in that the X-ray source 11 and the X-ray detector 12 are attached to a bracket 17, the first holding device 13 holds the bracket 17 rotatably about a rotation center axis 16, the second holding device 14 is omitted, and the rotating table 15 is fixed. Other than that, the configuration is the same as that of the above embodiment.

[0076] According to the fourth modification, it is easier to adjust the relative positions of the subject 40, the X-ray source 11, and the X-ray detector 12, compared to the CT apparatus of the above embodiment, and the burden of adjustment man-hours for the imaging system is reduced when imaging multiple points on only a part of the subject 40. Furthermore, since control of the rotating table is not required, the control is simplified.

[0077] All the numerical values ​​shown in the above embodiment are merely examples, and it goes without saying that other appropriate numerical values ​​can be used.

[0078] The above-described embodiment is merely an example in all respects. The present invention should not be construed as being limited by the description of the above-described embodiment. The present invention can be implemented in various other forms without departing from the spirit or main characteristics thereof. [Explanation of symbols]

[0079] 1...Correction value creation section 2…Subject photography department 3. Image location information 4...X-ray projection image correction value calculation means 5...X-ray projection image correction value (correction filter) 6...Correction value recording means 10 (10A to 10D)…imaging section 11...X-ray source 12…X-ray detector 13...First gripping device 14…Second gripping device 15...Rotary table 16...Rotation axis 17…Bracket 20...Control calculation section 21...imaging unit control means 22...Image collection means 24...X-ray projection image correction means 25...3D data reconstruction method 26...Image display means 30…Display device 40…Subject 61…Virtual point 62...Projected image 63…Reconstructed 3D data 64…Reprojection image 66…Projected image 67…Corrected image 68…imaging orbit 100...CT device 211...First gripping device control means 212...X-ray irradiation control means 213...Rotary table control means 214...detector control means 215...Second gripping device control means

Claims

1. A method for generating a correction filter used in reconstructing a three-dimensional X-ray CT image, comprising the steps of: Setting a virtual point in a virtual space; generating, in the virtual space, a projected image by projecting the virtual point at each of different imaging positions on an imaging trajectory; generating reconstructed 3D data based on the projection images in the virtual space; generating a reprojection image by projecting the reconstructed 3D data, which is a subject, for each of the imaging positions in the virtual space; performing a first Fourier transform on the projection images; performing a second Fourier transform on the reprojected image; calculating a correction value for each imaging position based on the projection image after the first Fourier transform and the reprojection image after the second Fourier transform; and storing the imaging position and the correction value in association with each other.

2. The first Fourier transform is performed using the following formula: The second Fourier transform is performed using the following formula: The calculation of the correction value is performed using the following formula:

2. The method for generating a correction filter according to claim 1, wherein in each of the above equations, variables x and y correspond to coordinates of the projected image or the reprojected image, variable θ corresponds to an imaging attitude, variables u and v correspond to frequency components after Fourier transform, function p(x, y, θ) corresponds to a projected image, and function P(u, v, θ) corresponds to the reprojected image.

Images