Method for generating correction filters

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 Art

[0002] A CT (Computed Tomography) apparatus that generates a tomographic image of a human body or the like using an X-ray source and an X-ray detector is known (see, for example, Patent Document 1).

[0003] When reconstructing 3D data by the FBP (Filtered Back Projection) method in a CT apparatus, it is necessary to correct the projection image (radiograph) in order to eliminate blurring (noise of low-frequency components) of the reconstructed image. In a general CT apparatus, since the imaging orbits of the X-ray source and the X-ray detector are circular, the required correction filter can be theoretically calculated.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, in a CT apparatus with a free orbit (non-circular orbit) imaging path, in order to avoid robot errors and interference with the subject, a situation occurs where the imaging paths of the X-ray source and the X-ray detector do not form a circle. In such a case where the imaging path is a free orbit (non-circular orbit), the noise appearing due to reconstruction has an irregular shape, and there is a problem that an optimal correction filter cannot be calculated by the same method as 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 with a free orbit. [Means for solving the problem]

[0007] The method for generating a correction filter according to this disclosure is a method for generating a correction filter used when reconstructing a three-dimensional X-ray CT image, and comprises the steps of: setting virtual points in a virtual space; generating a projection image in the virtual space by projecting the virtual points onto each of the different imaging positions on the imaging trajectory; generating reconstructed 3D data in the virtual space based on the projection image; generating a reprojection image in the virtual space by projecting the reconstructed 3D data, which is the subject, onto each of the imaging positions; performing a first Fourier transform on the projection image; performing a second Fourier transform on the reprojection image; calculating a correction value for each of the imaging positions based on the projection image after the first Fourier transform and the reprojection image after the second Fourier transform; and storing the imaging positions and the correction value in association.

[0008] This configuration provides a method for generating a correction filter suitable for CT reconstruction where the imaging trajectory is a free trajectory.

[0009] Furthermore, in the above method for generating the correction filter, the first Fourier transform is performed using the following equation: The second Fourier transform of TIFF0007893225000001.tif20110 is performed using the following formula: TIFF0007893225000002.tif21113 The calculation of the correction value is performed using the following formula: In the above formulas, 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 orientation, the variables u and v may correspond to the frequency components after the 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. [Effects of the Invention]

[0010] This disclosure provides a method for generating a correction filter suitable for CT reconstruction where the imaging trajectory is a free trajectory. [Brief explanation of the drawing]

[0011] [Figure 1] This is a configuration diagram of a CT apparatus 100 in which the correction filter generation method according to the embodiment is implemented. [Figure 2] (a) A flowchart for calculating the correction value, and (b) A flowchart for correcting the projected image of the subject that was actually captured. [Figure 3] (a) to (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, (c) Conceptual diagram of conversion between two-dimensional and three-dimensional coordinates. [Figure 5] (a) An example of imaging unit 10A, which is a modified example 1 of imaging unit 10, and (b) An example of imaging unit 10B, which is a modified example 2 of imaging unit 10. [Figure 6] (a) An example of imaging unit 10C, which is a modified example 3 of imaging unit 10, and (b) An example of imaging unit 10D, which is a modified example 4 of imaging unit 10. [Modes for carrying out the invention]

[0012] The method for generating a correction filter, which is an embodiment of the present invention, will be described below with reference to the attached drawings. In each figure, corresponding components are denoted by the same reference numerals, and redundant explanations are omitted.

[0013] Figure 1 is a diagram showing the configuration of a CT apparatus 100 (X-ray CT apparatus) in which the correction filter generation method according to the embodiment is implemented.

[0014] As shown in FIG. 1, the CT apparatus 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 apparatus 100 may be a cone beam CT apparatus or another CT apparatus such as a helical CT apparatus. The correction value creation unit 1 may be built in the CT apparatus 100 or provided outside the CT apparatus 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, when a processor executes a predetermined program read from a storage unit (for example, ROM) into a memory (for example, RAM). Some or all of these may be realized by hardware. Note that the processor, the storage unit, and the memory may be built in the CT apparatus 100 or provided outside the CT apparatus 100.

[0016] The correction value calculation means 4 calculates the correction value 5 based on the imaging position information 3 at the time of projection image imaging, that is, the actual position information of each of the X-ray source 11 and the X-ray detector 12 when the projection image is imaged. The processing 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 apparatus 100 or provided outside the CT apparatus 100.

[0018] The subject imaging unit 2 includes an imaging unit 10, a control arithmetic unit 20, and a display device 30.

[0019] The imaging unit 10 arranges the subject 40 on a rotary table 15 that is a rotating means to obtain 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 rotary table 15.

[0021] The X-ray source 11 irradiates the subject 40, which is placed on the 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). For example, a robot with multiple joints (industrial robot) may be used as the first gripping device 13.

[0023] The X-ray detector 12 detects the X-rays that have passed through the subject 40. The X-ray detector 12 then outputs an X-ray projection image of the subject 40 (X-ray projection image), which is X-ray projection image data. The projection image is input to the control calculation unit 20.

[0024] The X-ray detector 12 can have any configuration as long as it can obtain a two-dimensional image of the subject 40, which is the projected image. For example, the X-ray detector 12 may be a flat panel detector that obtains a two-dimensional image of the subject 40, which is the projected image; it 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 it 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 within the imaging system (imaging unit 10) so that it is positioned opposite the X-ray source 11. For example, a multi-jointed robot (industrial robot) may be used as the second gripping device 14.

[0026] The rotary table 15 rotates around the rotation axis 16 with the subject 40 placed on it. As a result, the X-ray source 11 and X-ray detector 12 move relative to the subject 40, allowing the subject 40 to be imaged from multiple directions and projected images of the imaged subject 40 to be obtained.

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

[0028] The control calculation unit 20 includes an imaging unit control means 21, an image acquisition 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 acquisition means 22, the X-ray projection image correction means 24, the 3D data reconstruction means 25, and the image display means 26 are implemented, for example, by a processor executing a predetermined program (not shown) read from a storage unit (e.g., ROM) into memory (e.g., RAM). Some or all of these may be implemented by hardware. The processor, storage unit, and memory may be the same as the processor, storage unit, and memory that implement the X-ray projection image correction value calculation means 4 and the correction value recording means 6, or they may be different processors, storage units, and memories.

[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 rotary 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 posture of the first gripping device 13 that 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 status, etc.). The rotary table control means 213 controls the rotary table 15 on which the subject 40 or calibration jig (not shown) is placed to rotate (360-degree rotation) around the rotation axis 16. The detector control means 214 controls the conditions for acquiring the projection image by the X-ray detector 12. The second gripping device control means 215 controls the posture of the second gripping device 14 that grips the X-ray detector 12.

[0031] The image acquisition means 22 collects the projection image output by the X-ray detector 12 and stores it in a storage device (not shown). The X-ray projection image correction means 24 corrects the projection image collected by the image acquisition means 22 and stored in the storage device (not shown) based on the correction value 5 for each projection image (imaging position) obtained by the correction value creation unit 1 and stored in the storage device (not shown). The 3D data reconstruction means 25 reconstructs the projection image corrected by the X-ray projection image correction 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.) at the time the projection image was captured. The image display 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, which displays the 3D data (three-dimensional image) that has been reconstructed as described above.

[0033] The correction filter generation method of this 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 in a given imaging trajectory, based on pre-measured positional information of the X-ray source 11 and X-ray detector 12. Since the process is performed using an analytical method, it does not require iterative calculations. Therefore, this correction filter generation method can be implemented with low-cost equipment.

[0034] When reconstructing 3D data using the FBP method in a CT scanner, it is necessary to apply correction to the projected image to eliminate 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.

[0035] However, in a CT scanner 100 with the equipment configuration shown in Figure 1, the imaging trajectories of the X-ray source 11 and X-ray detector 12 are not circular in order to avoid errors in the robot (first grasping device 13, second grasping device 14, etc.) and interference with the subject 40. When the imaging trajectory is a free trajectory (non-standard trajectory) in this way, the noise that appears after reconstruction has an irregular shape, and it is not possible to calculate the optimal correction filter using the same method as the FBP method.

[0036] While iterative approximation methods exist that do not require correction filters, their nature of repeatedly performing feedback to obtain approximate values ​​results in extremely high computational costs. Therefore, they require large-scale computers or enormous computation time, posing a practical challenge.

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

[0038] Figure 2(a) is a flowchart for calculating the correction value, which is performed in a virtual space (three-dimensional space) by the correction value calculation means 4.

[0039] As a prerequisite, imaging operation data for the first gripping device 13 and the second gripping device 14 are created in advance, and imaging position information 3, which is information on the relative position (relative coordinates; see Figure 4(a)) and relative angle (see Figure 4(b)) of the X-ray source 11 and X-ray detector 12 with respect to the subject 40 in each imaging posture, is obtained. Figure 4(a) is a conceptual diagram of relative coordinates, and Figure 4(b) is a conceptual diagram of relative angles. The imaging operation data is data that defines the imaging trajectory. The imaging operation data includes information on the angles of the robot's axes (joints), the imaging signal to the X-ray detector 12, and the interlock signals between robots (e.g., imaging is complete and it is OK to move to the next posture, movement is complete and it is OK to take an image). The imaging operation data is used, for example, when the correction value calculation means 4 performs the processes in 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 projected image (correction image 67) after step S24 described later. In either case, a conversion between two-dimensional and three-dimensional coordinates is performed (see Figure 4(c)). This conversion itself can be performed using, for example, known techniques provided by OpenCV (Intel). Figure 4(c) is a conceptual diagram of the conversion between two-dimensional and three-dimensional coordinates.

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

[0041] Figures 3(a) to 3(c) are conceptual diagrams of the correction value calculation means 4. Figures 3(a) to 3(c) represent slice displays of one cross-section of the virtual space. Figure 3(a) represents the concept of step S10. In Figure 3(a), reference numeral 61 represents a virtual point set in the virtual space. Also, reference numeral 68 in Figure 3(a) represents the imaging trajectory (free trajectory) during imaging. In the general FBP method, images are taken around the subject in a circular trajectory. On the other hand, in this embodiment, cases such as a partially incomplete circular trajectory or a free trajectory (non-standard trajectory) where the imaging trajectory is not circular are conceivable. In Figure 3(a), reference numeral 62 represents the projected images taken at each position P1 to P5 along the imaging trajectory 68.

[0042] Next, reconstructed 3D data 63 is generated from the projected image 62 (step S11). That is, in a virtual space, reconstructed 3D data 63 (see Figure 3(b)) is generated based on the projected image 62 generated in step S10. Specifically, the projected 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) where the brightness decreases inversely proportional to the distance from the image. In the FBP method, since the blurring is uniform, blurring is corrected by using a Ram-Lak filter or the like as a reconstruction filter. On the other hand, as shown in Figure 3(a), when the imaging trajectory is a free trajectory (non-standard trajectory) that is not circular, the form of blurring is not uniform, as in the reconstructed 3D data 63, so sufficient correction cannot be achieved with the same filters as in the FBP method.

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

[0044] In this embodiment, a correction filter is generated by performing steps S12 and S13 to eliminate this blurring.

[0045] First, a reprojection image 64 is generated from the reconstructed 3D data 63 (step S12). That is, as shown in Figure 3(b), the reconstructed 3D data 63 generated in step S11 is reprojected to generate multiple reprojection images 64. At this time, the relative positions of the subject, the reconstructed 3D data 63, 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 (multiple) and the reprojection images 64 (multiple) have the same imaging orientation at each position along the imaging trajectory 68 (for example, each position P1 to P5), but differ in the presence or absence of image blurring due to reconstruction.

[0046] Next, a Fourier transform is performed on the projected image 62 and the reprojected image 64, and a correction value 5 (correction amount) is calculated based on the ratio in frequency space (step S13).

[0047] The Fourier transform of the projection image 62 is performed using the following discrete Fourier transform formula, since the projection image 62 is discrete. Here, x and y are the coordinates of the projection image 62, θ is the imaging orientation, u and 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 image 62) taken. Note that θ does not represent an angle, but rather the "θth projection image (projection image 62) taken". In other words, the projection image θ=1 is the projection image taken at imaging position P1, as shown in "Example of recorded correction values" in Figure 1, the projection image θ=2 is the projection image taken at imaging position P2, and so on. Note that the imaging positions (for example, positions P1 to P5) are determined by the information in Figures 4(a) and 4(b).

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[0048]

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[0049]

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[0050] Next, the processing of the X-ray projection image correction means 24 will be explained according to Figure 2(b).

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

[0052] First, each time a projection image 66 is captured (or each time a projection image 66 is read out) as described above, a correction value 5 corresponding to that projection image 66 and its imaging position is retrieved (step S20). That is, a correction value 5 generated in the same posture as the imaging posture from 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 projected image 66 (step S21). The Fourier transform of the projected image 66 is performed using the following equation, where the function q(x, y, θ) corresponds to the projected image 66 and the function Q(u, v, θ) corresponds to the projected image 66 after the Fourier transform. N represents the total number of images taken of the projected image (projected image 66).

[0054]

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

[0056]

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[0057]

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[0058] As described above, this embodiment provides a method for generating a correction filter 5 suitable for CT reconstruction where the imaging trajectory is a free trajectory.

[0059] Furthermore, according to this embodiment, it becomes possible to generate and reconstruct a suitable reconstruction filter for a free-trajectory shooting orientation, thereby obtaining clear data.

[0060] Next, we will explain the variations.

[0061] <Example 1> First, we will describe the imaging unit 10A, which is a modified example of the imaging unit 10.

[0062] Figure 5(a) shows an example of the imaging unit 10A, which is a modified example of the imaging unit 10.

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

[0064] According to Modification 1, the range of motion of the first gripping device 13 and the second gripping device 14 restricts the rotation angle of imaging, resulting in a range of less than 360 degrees and potentially reducing the amount of data during reconstruction. However, the imaging unit 10 of the above embodiment can image larger subjects 40 that cannot be rotated.

[0065] <Modification 2> Next, we will describe the imaging unit 10B, which is a modified example of the imaging unit 10.

[0066] Figure 5(b) shows an example of the imaging unit 10B, which is a modified example of the imaging unit 10.

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

[0068] According to Modification 2, compared to the CT apparatus of the above embodiment, the relative positions of the subject 40, the X-ray source 11, and the X-ray detector 12 are easier to adjust, and the burden of adjusting the imaging system is reduced when imaging only a part of the subject 40 at multiple locations.

[0069] <Variation 3> Next, we will describe the imaging unit 10C, which is a modified example 3 of the imaging unit 10.

[0070] Figure 6(a) shows an example of the imaging unit 10C, which is a modified example 3 of the imaging unit 10.

[0071] The imaging unit 10C differs from the imaging unit 10 of the above embodiment in that the X-ray source 11 and X-ray detector 12 are mounted on the bracket 17, the first gripping device 13 grips the bracket 17, the second gripping device 14 grips the subject 40 so that it can rotate around the rotation center axis 16, and the rotary table 15 is omitted. Otherwise, the configuration is the same as in the above embodiment.

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

[0073] <Modification 4> Next, we will describe the imaging unit 10D, which is a modified example of the imaging unit 10.

[0074] Figure 6(b) shows an example of the imaging unit 10D, which is a modified example 4 of the imaging unit 10.

[0075] The imaging unit 10D differs from the imaging unit 10 of the above embodiment in that the X-ray source 11 and X-ray detector 12 are mounted on the bracket 17, the first gripping device 13 grips the bracket 17 so that it can rotate around the rotational axis 16, the second gripping device 14 is omitted, and the rotary table 15 is fixed. Otherwise, the configuration is the same as in the above embodiment.

[0076] According to Modification 4, compared to the CT apparatus of the above embodiment, the relative positions of the subject 40, the X-ray source 11, and the X-ray detector 12 are easier to adjust, and the burden of adjusting the imaging system is reduced when imaging multiple locations on only a part of the subject 40. Furthermore, control is simplified because control of the rotary table is unnecessary.

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

[0078] The embodiments described above are merely illustrative in all respects. The invention is not to be construed as being limited by the descriptions of the embodiments above. The invention can be carried out in various other ways without departing from its spirit or main features. [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~10D)...Imaging Unit 11...X-ray source 12…X-ray detector 13...First gripping device 14…Second gripping device 15… Rotating table 16…Center of rotation axis 17…Bracket 20...Control calculation unit 21…Imaging Unit Control Means 22…Image collection methods 24...X-ray projection image correction means 25... 3D data reconstruction means 26…Means for displaying images 30…Display device 40…Subject 61…Virtual point 62…Projection image 63…Reconstructed 3D data 64…Reprojection image 66…Projection 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 when reconstructing a three-dimensional X-ray CT image, The steps include setting a virtual point in a virtual space, In the virtual space, the steps include generating a projected image by projecting the virtual points onto each of the different imaging positions on the imaging trajectory, The steps include generating reconstructed 3D data based on the projected image in the virtual space, In the virtual space, the step of generating a reprojected image by projecting the reconstructed 3D data, which is the subject, onto each imaging position, The steps include performing a first Fourier transform on the projected image, The steps include performing a second Fourier transform on the aforementioned reprojected image, A step of 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, A method for generating a correction filter, comprising the step of storing the image position and the correction value in association.

2. The first Fourier transform described above is performed using the following equation: The second Fourier transform described above is performed using the following equation: The calculation of the aforementioned correction value is performed using the following formula: In each of the above equations, the variables x and y correspond to the coordinates of the projected image or the reprojected image, the variable θ corresponds to the imaging orientation, the variables u and v correspond to the frequency components after the Fourier transform, the function p(x, y, θ) corresponds to the projected image, and the function P(u, v, θ) corresponds to the reprojected image, respectively, a method for generating a correction filter according to claim 1.

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