A method for reducing high-density object artifacts in limited-view tomography

Abstract

The present invention discloses a method for reducing high-density object artifacts in limited-view tomography, comprising: placing an X-ray emitter and a receiver respectively above and below a target tissue; moving the X-ray emitter around the tissue within a limited angle and acquiring projection data; using a zero matrix as the background value in the initial iterative algorithm; based on the set background value, independently updating the reconstructed image obtained in the previous iteration according to the improved SART algorithm at each scanning angle and saving the updated image data; traversing the saved image data updated at all scanning angles, selecting the non-zero minimum value at the corresponding position in the reconstructed image of each scanning angle for each voxel point, and taking zero if all are zero as the final result of this voxel in this iteration; using the final result of this iteration as the background value for the next iteration; repeating the iteration to obtain a limited-angle CT reconstructed image with reduced high-density object artifacts.

Description

Technical Field

[0001] The present invention relates to a method for reducing artifacts of high-density objects, in particular to a method for reducing artifacts of high-density objects in limited-view tomography. Background Art

[0002] Traditional CT (Computed Tomography) imaging technology uses a cone-shaped X-ray emitter to rotate 180° around the target tissue, emit X-rays at regular intervals, and receive signals on the other side of the target tissue through an X-ray receiver, thereby obtaining several sets of projection data. The internal structure of the target tissue is reconstructed based on the characteristic that different parts of the target tissue have different absorption or attenuation coefficients for X-rays.

[0003] In actual use, due to the differences in the target tissue structure and the constraints of the application environment, it is usually difficult to achieve full-angle scanning of the target tissue. Therefore, limited-view CT imaging technology is often used in actual applications. Different from traditional CT technology that requires collecting a complete 180° data set, limited-view CT imaging technology usually reconstructs images based on projection data obtained within a limited angle range from 15° to 60°. Traditional limited-angle CT reconstruction methods include iterative algorithms and non-iterative algorithms. Non-iterative algorithms include the BP (Back Projection) algorithm and the FBP (Filtered BackProjection) algorithm. The BP algorithm has a fast reconstruction speed, but the quality of the reconstructed image is poor. The FBP algorithm uses a filter on the basis of the BP algorithm to filter out noise information in the BP reconstruction process, and can provide satisfactory image quality while having a fast calculation speed. However, this method is limited by the imaging geometry. For example, in some systems that use a very narrow projection angle range, non-uniform angle sampling schemes, and fixed detectors, the calculation of FBP is more complex, and the calculation error will also reduce the image quality. Iterative algorithms, such as the SART (Simultaneous Algebraic Reconstruction Technique) algorithm, and statistical model-based algorithms such as the ML-convex (Maximum Likelihood convex) algorithm, can adapt to limited-view tomography without being limited by geometry, and can effectively enhance the edges and contrast of the target tissue image. With the upgrade of computer hardware and the improvement of parallel computing efficiency, the reconstruction speed of iterative algorithms has also been improved to a certain extent. However, due to the limitations of the SART algorithm itself and the limited sampling angles, the SART algorithm cannot eliminate the overshoot, undershoot artifacts generated in the reconstruction of high-density objects, and the artifacts around high-density objects through iteration. Summary of the Invention

[0004] Objective of the Invention: The technical problem to be solved by the present invention is to provide a method for reducing artifacts of high-density objects in limited-view tomography in view of the deficiencies of the prior art.

[0005] To solve the above technical problem, the present invention discloses a method for reducing artifacts of high-density objects in limited-view tomography, comprising the following steps:

[0006] Step 1: Place an X-ray emitter and a receiver respectively above and below the target tissue.

[0007] Step 2: Use the X-ray emitter to move around the tissue within a limited angle and emit X-rays, while the receiver collects projection data.

[0008] Step 3: Use a zero matrix as the background value in the initial iterative algorithm.

[0009] Step 4: Based on the set background value, independently update the reconstructed image obtained in the previous iteration according to the improved SART algorithm at each scanning angle and save the updated image data.

[0010] Step 5: Traverse the image data saved after the update at all scanning angles in Step 4, select the non-zero minimum value at the corresponding position in the reconstructed image at each scanning angle for each voxel point, and if all are zero, take zero as the final result of this voxel in this iteration.

[0011] Step 6: Use the final result of this iteration as the background value for the next iteration.

[0012] Step 7: Repeat Steps 4 to 6 to obtain a limited-angle CT reconstructed image with reduced artifacts of high-density objects.

[0013] In the iterative formula of the SART algorithm in Step 4 of the present invention, the correction formula for the reconstructed image x' at each scanning angle is:

[0014]

[0015] Wherein, represents the value of the jth voxel after the (k + 1)th iteration, i is the serial number of the taken projection value, λ is a relaxation factor, and the convergence speed and reconstruction result are affected by changing λ; J represents the number of voxels passed through by each X-ray, 1 ≤ j ≤ J; m represents the number of times the jth voxel is updated in this iteration process, M i represents the total number of times the jth voxel is updated in this iteration process, 1 ≤ m ≤ M i , A m,j,i represents the weight of the jth voxel when the projection value serial number is i and the mth update in this iteration process; bm,i It represents the projection value collected in the i - direction of the projection value sequence at the m - th update.

[0016] In step 4 of the present invention, in the improved SART algorithm, the data updates at different scanning angles in a single iteration use the same background value That is, the final result obtained after the previous iteration.

[0017] In step 4 of the present invention, in the improved SART algorithm, the data updates at different scanning angles in the initial iteration use a blank background value.

[0018] In step 4 of the present invention, all the updated data at each scanning angle is stored as y k,i , which represents the data updated at the i - th scanning angle in the k - th iteration.

[0019] In step 4 of the present invention, based on the set background value, at each scanning angle, the reconstructed image obtained in the previous iteration is independently updated according to the improved SART algorithm, and the updated data is saved; among them, the iterative formula of the SART algorithm is improved, including:

[0020]

[0021] Among them, represents the reconstructed value of the j - th voxel at the i - th angle in the (k + 1) - th iteration, λ is the relaxation factor, and the convergence speed and reconstruction result are affected by changing λ; represents the value of the j - th voxel after the k - th iteration; J represents the number of voxels passed through by each X - ray, 1 ≤ j ≤ J; m represents the number of times the j - th voxel is updated in this iteration process, M i represents the total number of times the j - th voxel is updated in this iteration process, 1 ≤ m ≤ M i , A m,j,i represents the weight of the j - th voxel at the i - th projection value sequence during the m - th update in this iteration process; b m,i It represents the projection value collected in the i - direction of the projection value sequence at the m - th update.

[0022] In step 5 of the present invention, after all the updated data is stored, the updated data is traversed, and for each voxel point, the non - zero minimum value at the corresponding position in the reconstructed image of each scanning angle is selected to form the final reconstructed result x′ of this round of iteration; among them, the method for obtaining the final result in a single iteration of the SART algorithm is improved, including: for each voxel value take the non - zero minimum value in this set.

[0023] In step 1 of the present invention, the X-ray emitter is located above the receiver, and the X-rays emitted by the emitter cover the entire target tissue.

[0024] In step 2 of the present invention, the method of moving around the tissue includes: the X-ray emitter moves in an arc in a plane perpendicular to the receiver around the receiver, emits X-rays at regular intervals within a limited angle range, and at the same time the receiver receives the projection data.

[0025] Advantageous effects:

[0026] A method for reducing artifacts of high-density objects in limited-view tomography proposed by the present invention is based on the traditional SART reconstruction algorithm, and reduces the overshoot, undershoot artifacts generated in the reconstruction of high-density objects and the artifacts around high-density objects by improving the algorithm. Description of the drawings

[0027] The following further specifically describes the present invention in conjunction with the drawings and specific embodiments, and the above and / or other advantages of the present invention will become clearer.

[0028] Figure 1 is a flowchart of the method of the present invention.

[0029] Figure 2 is a schematic diagram of the projection data acquisition process of the present invention.

[0030] Figure 3 is a schematic diagram of the XY section of the reconstructed image after 5 iterations using the SART algorithm.

[0031] Figure 4 is a schematic diagram of the XY section of the reconstructed image after 5 iterations using the improved SART algorithm of the present invention. Specific embodiments

[0032] The present invention proposes a method for reducing artifacts of high-density objects in limited-view tomography, including the following steps:

[0033] Step 1, place an X-ray emitter and a receiver above and below the target tissue respectively; the X-ray emitter is located above the receiver, and the X-rays emitted by the emitter cover the entire target tissue.

[0034] Step 2, use the X-ray emitter to move around the tissue and emit X-rays within a limited angle, and at the same time the receiver collects projection data; the method of moving around the tissue includes: the X-ray emitter moves in an arc in a plane perpendicular to the receiver around the receiver, emits X-rays at regular intervals within a limited angle range, and at the same time the receiver receives the projection data.

[0035] Step 3: Use a zero matrix as the background value in the initial iteration algorithm;

[0036] Step 4: Based on the set background value, independently update the reconstructed image obtained from the previous iteration at each scanning angle according to the improved SART algorithm and save the updated image data;

[0037] For the iteration formula of the SART algorithm, the correction formula for the reconstructed image x′ at each scanning angle is:

[0038]

[0039] Where, represents the value of the j-th voxel after the (k + 1)-th iteration, i is the serial number of the projection value taken, λ is the relaxation factor, and the convergence speed and reconstruction result are affected by changing λ; J represents the number of voxels passed through by each X-ray, 1 ≤ j ≤ J; m represents the number of times the j-th voxel is updated during this iteration, and M i represents the total number of times the j-th voxel is updated during this iteration, 1 ≤ m ≤ M i , A m,j,i represents the weight of the j-th voxel when the projection value serial number is i and the m-th update during this iteration; b m,i represents the projection value collected in the direction of the projection value serial number i during the m-th update.

[0040] In the improved SART algorithm, the data update at different scanning angles during a single iteration uses the same background value That is, the final result obtained after the previous iteration.

[0041] In the initial iteration of the improved SART algorithm, the data update at different scanning angles uses a blank background value.

[0042] Store the updated data for all scanning angles and denote it as y k,i , representing the data updated at the i-th scanning angle during the k-th iteration.

[0043] Based on the set background value, independently update the reconstructed image obtained from the previous iteration at each scanning angle according to the improved SART algorithm and save the updated data; among them, the iteration formula of the SART algorithm is improved, including:

[0044]

[0045] Where, represents the reconstruction value of the j-th voxel at the i-th angle during the (k + 1)-th iteration, λ is the relaxation factor, and the convergence speed and reconstruction result are affected by changing λ; represents the value of the j-th voxel after the k-th iteration; J represents the number of voxels that each X-ray passes through, where 1 ≤ j ≤ J; m represents the number of times the j-th voxel is updated during this iteration, and M i represents the total number of times the j-th voxel is updated during this iteration, where 1 ≤ m ≤ M i , A m,j,i represents the weight of the j-th voxel when it is updated for the m-th time during this iteration when the projection value serial number is i; b m,i represents the projection value collected in the direction of the projection value serial number i when it is updated for the m-th time.

[0046] Step 5: Traverse the image data saved after the update at all scanning angles in Step 4. For each voxel point, select the non-zero minimum value at the corresponding position in the reconstructed image of each scanning angle. If all are zero, take zero as the final result of this voxel for this iteration;

[0047] After all the updated data is stored, traverse the updated data. For each voxel point, select the non-zero minimum value at the corresponding position in the reconstructed image of each scanning angle to form the final reconstructed result x′ of this round of iteration; among them, the method for obtaining the final result in a single iteration of the SART algorithm is improved, including: for each voxel value take the non-zero minimum value in this set.

[0048] When traversing the updated data, if all the values at the corresponding positions in the reconstructed images of each scanning angle selected by individual voxel points are zero, then take zero as the final reconstructed result of this voxel point for this round of iteration.

[0049] Step 6: Use the final result of this iteration as the background value for the next iteration;

[0050] Step 7: Repeat Steps 4 to 6 to obtain a limited-angle CT reconstructed image with reduced high-density object artifacts.

[0051] Embodiment

[0052] The embodiments of the present invention will be described below in conjunction with the accompanying drawings.

[0053] As Figure 1 shown, a method for reducing high-density object artifacts in limited-view tomography proposed by the present invention includes the following steps:

[0054] Step 1: Place an X-ray emitter and a receiver above and below the target tissue respectively;

[0055] Step 2: Use the X-ray emitter to move around the tissue and emit X-rays within a limited angle, and at the same time the receiver collects projection data;

[0056] Step 3: Use a zero matrix as the background value in the initial iteration algorithm.

[0057] Step 4: Based on the set background value, independently update the reconstructed image obtained from the previous iteration according to the SART algorithm at each scanning angle and save the updated data.

[0058] Step 5: Traverse the images saved after the update at all scanning angles in Step 4. For each voxel, select the non-zero minimum value at the corresponding position in the reconstructed images at each scanning angle. If all are zero, take zero as the final result of this voxel for this iteration.

[0059] Step 6: Use the final result of this iteration as the background value for the next iteration.

[0060] Step 7: Repeat Steps 4 - 6 to obtain a limited-angle CT reconstructed image with reduced high-density object artifacts.

[0061] In this embodiment, in Step 1, the X-ray receiver is 23.04 cm long and 19.20 cm wide, and the size of each pixel is a square with a side length of 0.1 mm. Therefore, the projection data received each time is a planar graph with a resolution of 1920×2304. Place the target tissue between the X-ray emitter and the receiver, close to the receiver plane. The distance between the bottom surface of the object and the receiver plane is 2 cm, and the distance from the X-ray emitter to the rotation pivot is 64 cm. The placement positions of the X-ray emitter, receiver, and object are as Figure 2 shown.

[0062] In this embodiment, in Step 2, as Figure 2 shown, the center of the circular arc motion trajectory is at point P, and the rotation pivot P' is the projection of point P on the rotation axis. The initial position of the X-ray emitter is at the left endpoint L of the motion trajectory, and the motion end point is the right endpoint R. In the motion plane, the X-ray emitter rotates around point P' as the center of rotation, making an arc motion. The central angle of this arc is 60°, and the left endpoint L and the right endpoint R are symmetric about PP' and form an angle of 30° with the central axis respectively. The X-ray emitter moves from the left endpoint L to the right endpoint R in a circular arc motion, emits X-rays to the X-ray receiver once every 3°, and the data received by the receiver is used as a set of projection values for this angle. When the emitter reaches point R, the scanning process ends, and a total of 21 sets of projection data are collected.

[0063] In this embodiment, in Step 4, use the improved SART reconstruction algorithm to reconstruct the collected projection data. The SART algorithm solves for the solution x of a class of equations by iteration:

[0064] Ax = b (1)

[0065] In formula (1), A is an M×N matrix, which is the system matrix of the projection transformation during the image reconstruction process. x is an N-dimensional column vector, composed of the values of the voxels to be reconstructed, representing the attenuation coefficient of each voxel in the target tissue for X-rays. N is the number of reconstructed voxels, b is an M-dimensional column vector representing the projection values, and M is the total number of acquired projection pixels. In limited-angle CT imaging, generally the value of M is much smaller than N, so this equation has an infinite number of solutions. The SART algorithm first gives an initial estimated value x′ to x, then projects this estimated value to obtain an estimated value b′ of the projection vector b, and then uses the difference b 1 between b and b′, b 1 -b′, as the correction value to correct x′. Completing one correction of x′ for all 21 groups of projection values is regarded as one iteration. Finally, x′ converges to the x that makes the smallest, that is, the least squares solution.

[0066] According to the SART algorithm theory, the introduction of the weighting matrix W can effectively reduce artifacts. Therefore, it is necessary to find the value of x that minimizes the following loss function L(x), as shown in formula (2):

[0067]

[0068] Using the gradient descent method to find the x that minimizes L(x) gives the SART algorithm iteration formula. The correction formula for each scanning angle to the reconstructed image x′ is:

[0069]

[0070] where, represents the value of the j-th voxel after the (k + 1)-th iteration. i is the serial number of the taken projection value, λ is the relaxation factor, and the convergence speed and reconstruction result are affected by changing λ; J represents the number of voxels passed by each X-ray, 1 ≤ j ≤ J; m represents the number of times the j-th voxel is updated during this iteration, and M i represents the total number of times the j-th voxel is updated during this iteration, 1 ≤ m ≤ M i , A m,j,i represents the weight of the j-th voxel when the projection value serial number is i and the m-th update during this iteration; b m,i represents the projection value acquired in the direction of the projection value serial number i during the m-th update.

[0071] We made two changes to the above algorithm to achieve the purpose of reducing artifacts of high-density objects in the reconstructed image:

[0072] First, when given an initial estimated value x′, the initial data used at each scanning angle is unique, and the final result of the previous iteration is selected. In particular, a blank vector is used for the first iteration.

[0073] Second, the correction of x′ at each scanning angle is independent. Denote the updated data of all scanning angles as y i , which represents the updated data at the i-th scanning angle. After all 21 groups of updated data are stored, traverse these 21 groups of updated data, and for each voxel, select the minimum non-zero value (take zero if all are zero) at the corresponding position in the reconstructed image of each scanning angle to form the final result x′ of this round of iteration. The improved formula is as follows:

[0074]

[0075] Among them, represents the reconstructed value of the j-th voxel at the i-th angle in the (k + 1)-th iteration. λ is the relaxation factor, and the convergence speed and reconstruction result are affected by changing λ. represents the value of the j-th voxel after the k-th iteration. J represents the number of voxels passed through by each X-ray, 1 ≤ j ≤ J; m represents the number of times the j-th voxel is updated in this iteration process, and M i represents the total number of times the j-th voxel is updated in this iteration process, 1 ≤ m ≤ M i , A m,j,i represents the weight of the j-th voxel at the m-th update in this iteration when the projection value serial number is i; b m,i represents the projection value collected in the direction of the projection value serial number i at the m-th update. To ensure convergence, λ is taken as 0.1 in this example, and the iteration is performed 5 times. To speed up the operation, the projection data is scaled down proportionally to a resolution of 480×576.

[0076] In this embodiment, in step 5, traverse the images saved after the update at all scanning angles in step 4, and for each voxel, select the non-zero minimum value at the corresponding position in the reconstructed image of each scanning angle. If all are zero, take zero as the final result of this voxel in this iteration. The specific operation steps are Take the non-zero minimum value in this set. If all 21 elements in this set are zero, then take zero.

[0077] As Figure 3 shown, it is a schematic diagram of the XY section of the reconstructed image after 5 iterations using the SART algorithm, and as Figure 4As shown in the figure, it is a schematic diagram of the XY section of the reconstructed image after 5 iterations of the improved SART algorithm using the present invention. It can be clearly seen that by using the method of the present invention to improve the SART algorithm, the overshoot, undershoot artifacts generated in the reconstruction of high-density objects and the artifacts around high-density objects are reduced.

[0078] The present invention provides an idea and method for reducing high-density object artifacts in limited-view tomography. There are many methods and ways to specifically implement this technical solution. The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by existing technologies.

Claims

1. A method for reducing artifacts of high-density objects in limited-view tomography, characterized in that, it includes the following steps: Step 1, place an X-ray emitter and a receiver respectively above and below the target tissue; Step 2, use the X-ray emitter to move around the tissue within a limited angle and emit X-rays, while the receiver collects projection data; Step 3, use a zero matrix as the background value in the initial iterative algorithm; Step 4, based on the set background value, independently update the reconstructed image obtained in the previous iteration according to the improved SART algorithm at each scanning angle and save the updated image data; Step 5, traverse the image data saved after the update at all scanning angles in Step 4, select the non-zero minimum value at the corresponding position in the reconstructed image of each scanning angle for each voxel point, and if all are zero, take zero as the final result of this voxel in this iteration; Step 6, use the final result of this iteration as the background value for the next iteration; Step 7, repeat Steps 4 to 6 to obtain a limited-angle CT reconstructed image with reduced artifacts of high-density objects; Among them, for the iterative formula of the SART algorithm in Step 4, the correction formula for the reconstructed image x′ at each scanning angle is: Among them, represents the value of the j-th voxel after the (k + 1)-th iteration. i is the serial number of the taken projection value, λ is the relaxation factor, and the convergence rate and reconstruction result are affected by changing λ; J represents the number of voxels passed through by each X-ray, 1 ≤ j ≤ J; m represents the number of times the j-th voxel is updated during this iteration, and M i represents the total number of times the j-th voxel is updated during this iteration, 1 ≤ m ≤ M i , A m,j,i represents the weight of the j-th voxel when it is updated for the m-th time during this iteration when the projection value serial number is i; b m,i represents the projection value collected in the direction of the projection value serial number i when it is updated for the m-th time.

2. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 1, characterized in that, In step 4, the improved SART algorithm uses the same background value for data update at different scanning angles in a single iteration. That is, the final result obtained after the previous iteration.

3. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 2, characterized in that, In Step 4, the improved SART algorithm uses a blank background value for data update at different scanning angles in the initial iteration.

4. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 3, characterized in that, In step 4, all the data after the scanning angle update is stored and denoted as y k,i , representing the data after the update of the i-th scanning angle in the k-th iteration; y k,i is an N-dimensional column vector, consisting of N elements, where N represents the number of reconstructed voxels.

5. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 4, characterized in that, In Step 4, based on the set background value, independently update the reconstructed image obtained in the previous iteration according to the improved SART algorithm at each scanning angle and save the updated data; Among them, the improvement of the iterative formula of the SART algorithm includes: Among them, represents the reconstruction value of the j-th voxel at the i-th angle in the (k + 1)-th iteration. λ is the relaxation factor, and the convergence speed and reconstruction result are affected by changing λ; represents the value of the j-th voxel after the k-th iteration; J represents the number of voxels that each X-ray passes through, 1 ≤ j ≤ J; m represents the number of times the j-th voxel is updated during this iteration, and M i represents the total number of times the j-th voxel is updated during this iteration, 1 ≤ m ≤ M i , A m,j,i represents the weight of the j-th voxel when it is updated for the m-th time during this iteration when the projection value serial number is i; b m,i represents the projection value collected in the direction of the projection value serial number i when it is updated for the m-th time.

6. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 5, characterized in that, In Step 5, after all the updated data is stored, traverse the updated data, and select the non-zero minimum value at the corresponding position in the reconstructed image of each scanning angle for each voxel point to form the final reconstructed result x′ of this round of iteration; Among them, the method for obtaining the final result in a single iteration of the SART algorithm is improved, including: for each voxel value take the non-zero minimum value in this set.

7. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 6, characterized in that, In Step 5, when traversing the updated data, if all the values at the corresponding positions in the reconstructed image of each scanning angle selected for individual voxel points are zero, then take zero as the final reconstructed result of this voxel point in this round of iteration.

8. A method for reducing artifacts of high-density objects in limited-view tomography according to Claim 7, characterized in that, In step 1, the X-ray emitter is located above the receiver, and the X-rays emitted by the emitter cover the entire target tissue.

9. A method for reducing artifacts of high-density objects in limited-view tomography according to claim 8, characterized in that the method of moving around the tissue in step 2 includes: the X-ray emitter moves in an arc in a plane perpendicular to the receiver around the receiver, emits X-rays at regular intervals within a limited angular range, and at the same time the receiver receives projection data.

Images