Finite angle CT iterative reconstruction algorithm based on geometric feature constraint

Abstract

The invention discloses a finite angle CT (Computed Tomography) iterative reconstruction algorithm based on geometric feature constraint, which comprises the following steps of: extracting a geometric contour constraint condition from a standard workpiece for updating constraint data in a subsequent iteration process; defect limited angle projection data are obtained through operation between standard workpiece projection data and to-be-detected workpiece limited angle projection data, and on the basis, iterative reconstruction is firstly performed, and then projection is performed to obtain defect full-angle projection data. And combining the defect full-angle projection data with the standard workpiece full-angle projection data, and carrying out iterative reconstruction under geometric constraints to obtain an internal reconstruction image of the to-be-detected workpiece. According to the method, artifacts in the cone beam CT reconstruction image of the workpiece in the limited angle scanning range are effectively removed, and the task requirement for high-definition reconstruction of the internal image of the workpiece under limited angle scanning is met.

Description

Technical Field

[0001] The present invention belongs to the field of limited-angle CT scan reconstruction, and particularly relates to a limited-angle CT iterative reconstruction algorithm based on geometric feature constraints. Background Art

[0002] Industrial computed tomography technology based on X-rays is widely used in the internal structure image reconstruction of components in fields such as automobile manufacturing, aerospace, and energy equipment due to its characteristics of non-contact, strong penetration ability, and high detection accuracy. For the defects existing in multi-layer composite material structures, industrial CT can achieve defect size measurement and positioning through high-precision imaging.

[0003] When the CT scan angle is not restricted, the classic Filtered Back Projection (FBP, FDK in three-dimensional reconstruction) algorithm can quickly reconstruct the internal image of the workpiece through complete-angle projection data. However, in actual detection, due to workpiece size limitations, detection space constraints, or ray source position limitations, it is often only possible to collect projection data at a limited angle (such as 0 to 120°). In such cases, directly applying the FBP algorithm will result in serious strip artifacts and blurred details in the reconstructed image, unable to meet the high-precision detection requirements. Summary of the Invention

[0004] To solve the above problems, the present invention discloses a limited-angle CT iterative reconstruction algorithm based on geometric feature constraints, which can reconstruct a high-definition internal image of the workpiece under the condition of limited scan angles, is applicable to industrial scenarios such as in-situ detection and non-destructive evaluation, and overcomes the problem of reduced reconstruction quality caused by incomplete projection data.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A limited-angle CT iterative reconstruction algorithm based on geometric feature constraints, comprising the following steps:

[0007] S1: Calculate the geometric contour constraint condition L of this type of workpiece from the complete-angle (0 to 360°) CT scan projection data Projection of a standard and defect-free workpiece; std

[0008] S2: Perform data preprocessing on the limited-angle (0 to 120°) CT scan projection data Projection of the workpiece to be measured, and obtain the limited-angle projection Projection of the possible defects existing in the workpiece to be measured through the operation between Projection and Projection; limited std limited defects ;

[0009] S3: Use the limited-angle projection Projection of the defect defects Perform iterative reconstruction to obtain the three-dimensional reconstructed image Data of the defect defects ;

[0010] S4: Perform full-angle projection on the three-dimensional reconstructed image Data of the defect defects And combine it with the limited-angle projection Projection of the actual defect defects To obtain the full-angle projection Projection after complementing the defect defects-conpeleted ;

[0011] S5: Calculate the full-angle projection data Projection after complementing the workpiece by operating on the full-angle projection Projection after complementing the defect defects-conpeleted And the standard projection Projection of the workpiece std ; conpeleted ;

[0012] S6: Use Projection conpeleted To perform iterative reconstruction. In each iteration, use the geometric contour constraint L of this type of workpiece to limit and correct the iteration result, and obtain the three-dimensional reconstructed image Data of the workpiece to be measured recon .

[0013] Furthermore, the step S1 specifically includes the following steps

[0014] S1.1: Normalize the CT scan projection data Projection of the standard and defect-free workpiece for the full angle (0 - 360°) std Specifically, when the sampling angle interval is θ, Projection std Contains T = 360° / θ standard workpiece projection data x at different angles k , k = 0, 1, 2, 3…, T - 1; where the projection data x at each angle k Is a two-dimensional matrix with the shape of H×W, and H and W are the sizes of the detection plate; for any point point k In any x i,j,k , i ∈ [0, H - 1], j ∈ [0, W - 1], k ∈ [0, T - 1], count the minimum value V min = Min(point i,j,k ), the maximum value V max = Max(point i,j,k ); Then perform normalization using the following formula

[0015] S1.2: Use the standard projection data Projectionstd Perform FDK reconstruction to obtain the three-dimensional data Data of this type of workpiece std The cone-beam CT geometric model parameters used in the FDK reconstruction process, such as SOD, SDD, detector panel pixel size, object pixel size, projection angle interval, etc., are consistent with the data source;

[0016] S1.3: Manually select the workpiece geometric contour constraint condition L from the three-dimensional data Data of this type of workpiece std In order to make L fully cover the workpiece and at the same time maintain the binding force of L on the subsequent iterative reconstruction process, L is appropriately expanded outward on the basis of the actual geometric contour of the workpiece;

[0017] Furthermore, the step S2 specifically includes the following steps

[0018] S2: Take out the CT scan projection data from 0 to 120° from the standard projection data Projection std as the limited-angle standard projection Projection std2 , Projection std2 contains the standard workpiece projection data x of T / 3 different angles i , i = 0, 1, 2, 3…, T / 3 - 1, where T depends on the CT scan sampling interval. The limited-angle (0 to 120°) CT scan projection data Projection of the workpiece to be measured limited contains the projection data y of T / 3 different angles of the workpiece to be measured i , i = 0, 1, 2, 3…, T / 3 - 1; where the projection data x i or y i is a two-dimensional matrix with the shape of H×W, where H and W are the detector panel sizes. Let y i subtract the corresponding point data value of x i to obtain z i = y i - x i , i = 0, 1, 2, 3…, T / 3 - 1. The z i are combined to obtain the defect limited-angle projection Projection defects , and then perform normalization on Projection defects using the same normalization method as in S1.1;

[0019] Furthermore, the step S3 specifically includes the following steps

[0020] S3.1: For the projection data z of different angles in the defect limited-angle projection Projection defects i ​, i = 0, 1, 2, 3…, T / 3 - 1, is divided into 10 subsets according to the projection angle, and the division method is as follows: Subset Set1 = {z i | i = 0, 10, 20, 30,…, T / 3 - 10}, Subset Set2 = {z i | i = 1, 11, 21, 31,…, T / 3 - 9}, Subset Set3 = {z i | i = 2, 12, 22, 32,…, T / 3 - 8}, Subset Set 10 = {z i | i = 9, 19, 29, 39,…, T / 3 - 1};

[0021] S3.2: Use the Ordered Subsets Expectation Maximization (OS-EM) algorithm for reconstruction. Given an initial reconstructed image (a full-zero image), set the number of subsets of the OS-EM algorithm to 10 and set the maximum number of iterations. For each iteration, sequentially access each subset in order. For each subset, perform the following operations: Based on the current reconstructed image, calculate the expected value of the data corresponding to this subset; Update the reconstructed image according to the difference between this expected value and the actual measured value, and adjust the reconstructed image by minimizing the error. When the set maximum number of iterations is reached, the iteration is completed and the finally reconstructed image is output;

[0022] The iterative reconstruction algorithm used is as follows:

[0023]

[0024] Among them, represents the value of the k-th pixel point in the n-th iteration (i.e., the current estimate of the reconstructed image), and this value will be updated according to the projection data and the reconstruction process in each iteration, and finally converge to the estimated value of the real image;

[0025] represents the updated value of the k-th pixel point in the (n + 1)-th iteration. It is calculated from the previous iteration value and the factor adjusted through the expectation maximization step;

[0026] A ik is an element of the projection matrix, representing the contribution from the k-th pixel to the i-th projection data, which is calculated by the ray passing through the pixel point;

[0027] p i is the i-th projection data, which is the projection intensity collected from the CT scanner. Each projection data corresponds to the measurement value of the CT scanner at different angles and reflects the projection from the scanning angle i to the target object;

[0028] (Ax (n) ) iis the difference between the projection result of the reconstructed image after the nth iteration and the true projection data pi, which is used to calculate how to adjust the reconstructed image to make it closer to the true data;

[0029] is the sum of all projection data, representing the total contribution of the kth pixel to all projections, which is used to normalize the update factor to ensure that the update amplitude of each pixel is neither too large nor too small;

[0030] p i / (Ax (n) ) i is the projection data p i and the projection value (Ax (n) ) i obtained by the current reconstructed image through the projection matrix, representing the difference between the current reconstructed image and the true projection data.

[0031] Furthermore, the step S4 specifically includes the following steps

[0032] S4.1: Perform full-angle projection on the defective three-dimensional reconstructed image Data defects , using the cone-beam CT geometric model. The key parameters such as SOD, SDD, the number of detector pixels, pixel size, and angular interval are kept consistent with the data source device, and finally T projection data are obtained;

[0033] S4.2: The full-angle projection of the defect obtained in the previous step contains projection data F i , i = 0, 1, 2, 3…, T-1, while the actual limited-angle projection Projection defects of the defect contains projection data G i , i = 0, 1, 2, 3…, T / 3-1; Use the full-angle projection data of the defect to complement the actual limited-angle projection data of the defect to obtain the complemented full-angle projection data Projection defects-conpeleted of the defect, Projection defects-conpeleted contains projection data H i , i = 0, 1, 2, 3…, T-1, and the calculation formula of H i is as follows: when i ∈ [0, T / 3-1], H i = G i , when i ∈ [T / 3, T-1], H i = F i ;

[0034] Furthermore, the step S5 specifically includes the following steps

[0035] S5.1: The fully - complemented full - angle projection data Projection of the defect defects-conpeleted Contains projection data H from 0 to 360° i , i = 0, 1, 2, 3…, T - 1, the standard projection Projection of the workpiece std Contains projection data J from 0 to 360° i , i = 0, 1, 2, 3…, T - 1, the fully - complemented full - angle projection data Projection of the workpiece to be measured is obtained through the operation between the two conpeleted , Projection conpeleted Contains projection data L from 0 to 360° i , i = 0, 1, 2, 3…, T - 1, the calculation method is as follows: L i = H i + J i , i = 0, 1, 2, 3…, T - 1; the two - dimensional matrix L i Is obtained by adding the corresponding elements of J i And H i ;

[0036] S5.2: Normalize L i , i = 0, 1, 2, 3…, T - 1, the normalization method is the same as the normalization method in S1.1;

[0037] Furthermore, the step S6 specifically includes the following steps

[0038] S6.1: Divide the projection data x at different angles in the fully - complemented full - angle projection data Projection of the workpiece to be reconstructed conpeleted Into 10 subsets according to the projection angle, and the division method is as follows: subset Set1 = {x i |i = 0, 10, 20, 30,…, T / 3 - 10}; subset Set2 = {x i |i = 1, 11, 21, 31,…, T / 3 - 9}, subset Set3 = {x i |i = 2, 12, 22, 32,…, T / 3 - 8}, subset Set i = {x 10 |i = 9, 19, 29, 39,…, T / 3 - 1};

[0039] S6.2: Use the constrained OS - EM algorithm and the fully - complemented full - angle projection data Projection of the workpiece to be measured conpeleted For iterative reconstruction, the initial value of the iteration is directly using Projection limited k ​The result of FDK reconstruction is that in each iteration, geometric constraints are used to limit and correct the iteration result.

[0040] The improved iterative algorithm formula is as follows:

[0041]

[0042] Among them, λ k is the constraint factor, which is used to constrain the update of data during the iteration: when x k ∈L, λ k = 1, otherwise λ k = 0.

[0043] After reaching the set maximum number of iterations, the final three-dimensional reconstruction image of the workpiece to be measured is obtained.

[0044] The beneficial effects of the present invention are:

[0045] (1) An iterative reconstruction algorithm based on geometric contour constraints is proposed, effectively reducing the artifacts in the limited-angle CT reconstruction image.

[0046] (2) A method for completing the projection data under limited-angle CT scanning is proposed, supplementing the missing data under limited-angle CT scanning.

[0047] (3) A method for achieving high-definition imaging of workpieces under limited-angle CT scanning is proposed, effectively reducing the artifacts in the reconstructed image and improving the reconstruction quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is the flow schematic diagram of the present invention.

[0049] Among them, the left process is Process 1, and the right process is Process 2. Process 1 is the pre-work. For workpieces of the same type, Process 1 only needs to be executed once. When performing CT reconstruction on workpieces of this type later, the result of Process 1 can be used. Process 2 performs high-quality CT image reconstruction of the workpiece on the basis of Process 1.

[0050] Figure 2 is the comparison diagram of the reconstruction effect of the present invention under limited-angle scanning and the FDK reconstruction effect and the intermediate result diagram on the data of a certain type of workpiece.

[0051] Among them, (A) is the limited angle projection sinusoid of the standard workpiece, (B) is the full angle projection sinusoid of the standard workpiece, (C) is the result of FBP reconstruction using (B). (D) is the limited angle projection sinusoid of the defective workpiece, (G) is the limited angle projection sinusoid of the defect obtained in step 2, (H) is the full angle projection sinusoid of the defect obtained in steps 3 and 4 after completion, (E) is the full angle projection sinusoid of the defective workpiece obtained in step 5 after completion, and (I) is a slice of the 3D reconstructed image of the defective workpiece obtained in step 6. (F) is the reconstructed image of the workpiece obtained by directly using (D) for FBP reconstruction.

[0052] Figure 3 The figure is a comparison diagram of the reconstruction results of the limited angle CT scan of the present invention on the workpiece data set and the effects of other algorithms. DETAILED DESCRIPTION

[0053] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0054] Taking a hydrogen cylinder as an example, as shown in the figure, the limited angle CT iterative reconstruction algorithm based on geometric feature constraints described in the present invention includes the following steps:

[0055] S1: CT scan projection data from a full angle (0-360°) of a standard, defect-free hydrogen cylinder std Calculate the geometric contour constraint condition L of this type of hydrogen cylinder. The specific steps are as follows:

[0056] S1.1: Full angle (0-360°) CT scan projection data of a standard, defect-free hydrogen cylinder std Normalize the data; specifically, Projection std Contains 720 standard hydrogen cylinder projection data at different angles k , k = 0, 1, 2, 3…, 719, the CT scan sampling interval is 0.5°; the projection data x at each angle k is a two-dimensional matrix of shape 1024×1024; for any x k Any point in i,j,k ,i∈[0,1023],j∈[0,1023],k∈[0,719].Statistical minimum value V min =Min(point i,j,k ), maximum value V max =Max(point ,j,k ), and then normalized using the following formula:

[0057] S1.2: Use the standard projection data Projection std to perform FDK reconstruction to obtain the three-dimensional data Data of this type of hydrogen cylinder std , and the cone-beam CT geometric model parameters used in the FDK reconstruction process, such as SOD, SDD, detector panel pixel size, object pixel size, projection angle interval, etc., are consistent with the data source;

[0058] S1.3: Manually select the geometric contour constraint condition L of the hydrogen cylinder from the three-dimensional data Data of this type of hydrogen cylinder std . In order to make L fully cover the hydrogen cylinder and at the same time maintain the binding force of L on the subsequent iterative reconstruction process, L expands 5 voxel points outward on the basis of the actual geometric contour of the hydrogen cylinder;

[0059] S2: Perform data preprocessing on the limited-angle (0 - 120°) CT scan projection data Projection of the hydrogen cylinder to be measured limited to obtain the limited-angle projection Projection of the possible defects in the hydrogen cylinder to be measured through the operation between Projection std and Projection limited . The specific steps are as follows: defects

[0060] Take out the CT scan projection data from 0 to 120° in the standard projection data Projection std as the limited-angle standard projection Projection std2 . Projection std2 contains 240 standard hydrogen cylinder projection data x i , i = 0, 1, 2, 3…, 239. The limited-angle (0 - 120°) CT scan projection data Projection of the hydrogen cylinder to be measured limited contains 240 projection data y of the hydrogen cylinder to be measured at different angles i , i = 0, 1, 2, 3…, 239; where the projection data x i or y i at each angle is a two-dimensional matrix with a shape of 1024×1024. Let y i subtract the corresponding point data value of x i to obtain z i = y i - x i , i = 0, 1, 2, 3…, 240. The combination of z i obtains the defect limited-angle projection Projection defects . Then, perform operations on Projection defects ​Perform normalization in the same way as the normalization method in S1.1;

[0061] S3: Use the limited-angle projection of defects, Projection defects Perform iterative reconstruction to obtain the three-dimensional reconstructed image of the defect, Data defects , and the specific steps are as follows:

[0062] S3.1: Divide the projection data x at different angles in the limited-angle projection of defects, Projection defects , where i = 0, 1, 2, 3…, 239, into 10 subsets according to the projection angle. The division method is as follows: Subset Set1 = {x i |i = 0, 10, 20, 30,…, 229}, Subset Set2 = {x i |i = 1, 11, 21, 31,…, 230}, Subset Set3 = {x i |i = 2, 12, 22, 32,…231}, Subset Set i = {x 10 |i = 9, 19, 29, 39,…, 239}; i |i = 9, 19, 29, 39,…, 239};

[0063] S3.2: Use the ordered subsets expectation maximization (OS-EM) algorithm for reconstruction. Given an initial reconstructed image (a full-zero image), set the number of subsets of the OS-EM algorithm to 10 and the maximum number of iterations to 300. For each iteration, sequentially access each subset in order. For each subset, perform the following operations: Calculate the expected value of the data corresponding to this subset based on the current reconstructed image; Update the reconstructed image according to the difference between this expected value and the actual measured value, and adjust the reconstructed image by minimizing the error. In the iterative algorithm, the forward projection uses the ray-driven projection model with the ray step size set to 1 voxel; the back projection uses the pixel-driven projection model. When the set maximum number of iterations is reached, the iteration is completed and the finally reconstructed image is output;

[0064] The iterative reconstruction algorithm used is as follows:

[0065]

[0066] Among them, represents the value of the k-th pixel point in the n-th iteration (i.e., the current estimate of the reconstructed image), and this value will be updated in each iteration according to the projection data and the reconstruction process, and finally converge to the estimated value of the true image;

[0067] represents the updated value of the k-th pixel point in the (n + 1)-th iteration. It is obtained from the previous iteration value and calculated by factors adjusted through the expectation maximization step;

[0068] A ik is an element of the projection matrix, representing the contribution from the k-th pixel to the i-th projection data, calculated by a ray passing through the pixel point;

[0069] p i is the i-th projection data, which is the projection intensity collected from the CT scanner. Each projection data corresponds to the measurement value of the CT scanner at different angles and reflects the projection from the scanning angle i to the target object;

[0070] (Ax (n) ) i is the difference between the projection result of the reconstructed image after the n-th iteration and the true projection data pi, used to calculate how to adjust the reconstructed image to make it closer to the true data;

[0071] is the sum over all projection data, representing the total contribution of the k-th pixel to all projections, used to normalize the update factor to ensure that the update amplitude of each pixel is neither too large nor too small;

[0072] p i / (Ax (n) ) i is the projection data p i and the projection value (Ax (n) ) i obtained from the current reconstructed image through the projection matrix, representing the difference between the current reconstructed image and the true projection data;

[0073] S4: Perform full-angle projection on the defective three-dimensional reconstructed image Data defects and combine it with the actual defective limited-angle projection Projection defects to obtain the complemented full-angle projection Projection defects-conpeleted of the defect, and the specific steps are as follows:

[0074] S4.1: For the defective three-dimensional reconstructed image Data defectsPerform full-angle projection using a cone-beam CT geometric model of a standard and defect-free hydrogen cylinder. The parameters of the cone-beam CT geometric model used, such as SOD, SDD, detector panel pixel size, object pixel size, projection angle interval, etc., are consistent with the data source; SOD is 733 mm, SDD is 1466 mm, the voxel size is set to 0.2 mm, the number of voxels in the model is set to 512×512×512, the number of pixels on the detector panel is set to 1024×1024, and the projection sampling angle interval is 0.5°. The forward projection algorithm model used is the ray-driven projection model, and the ray step size is set to 1 voxel; finally, 720 projection data are obtained.

[0075] S4.2: The full-angle projection of the defect obtained in the previous step contains projection data F from 0 to 360° i , i = 0, 1, 2, 3…, 719, while the actual limited-angle projection Projection of the defect defects contains projection data G from 0 to 120° i , i = 0, 1, 2, 3…, 239; Use the full-angle projection data of the defect to complement the actual limited-angle projection data of the defect to obtain the complemented full-angle projection data Projection of the defect defects-conpeleted , Projection defects-conpeleted contains projection data H from 0 to 360° i , i = 0, 1, 2, 3…, 719, H i The calculation formula is as follows: When i ∈ [0, 239], H i = G i , when i ∈ [239, 719], H i = F i ;

[0076] S5: Perform an operation on the full-angle projection Projection of the defect defects-conpeleted and the standard projection Projection of the hydrogen cylinder std to obtain the complemented full-angle projection data Projection of the hydrogen cylinder to be reconstructed, and the specific steps are as follows: conpeleted

[0077] S5.1: The complemented full-angle projection data Projection of the defect defects-conpeleted contains projection data H from 0 to 360° i , i = 0, 1, 2, 3…, 719, and the standard projection Projection of the hydrogen cylinder std contains projection data J from 0 to 360° i , i = 0, 1, 2, 3…, 719. Through the operation between the two, the complemented full-angle projection data Projection of the hydrogen cylinder to be reconstructed is obtained.conpeleted , Projection conpeleted contains projection data L from 0 to 360°, i , i = 0, 1, 2, 3…, 719, and the calculation method is as follows: L i = H i + J i , i = 0, 1, 2, 3…, 719, the two-dimensional matrix L i is obtained by adding the corresponding elements of J i and H i ;

[0078] S5.2: Normalize L i , i = 0, 1, 2, 3…, 719, using the same normalization method as in S1.1;

[0079] S6: Use Projection conpeleted for iterative reconstruction. In each iteration, use geometric constraints to limit and correct the iterative results to obtain the three-dimensional reconstructed image dATA of the hydrogen cylinder to be reconstructed recon , and the specific steps are as follows:

[0080] S6.1: Divide the projection data xi at different angles in the full-angle projection data Projection of the hydrogen cylinder to be reconstructed conpeleted , i = 0, 1, 2, 3…, 719, into 10 subsets according to the projection angle, and the division method is as follows: subset Set1 = {x i |i = 0, 10, 20, 30,…, 710}, subset Set2 = {xi|i = 1, 11, 21, 31,…, 711}, subset Set3 = {x i |i = 2, 12, 22, 32,…, 718}, subset Set 10 = {x i |i = 9, 19, 29, 39,…, 719};

[0081] S6.2: Use the OS-EM algorithm with constraints for reconstruction. The parameters of the cone-beam CT geometric model used, such as SOD, SDD, detector panel pixel size, object pixel size, projection angle interval, etc., are consistent with the data source; SOD is 733mm, SDD is 1466mm, the voxel size is set to 0.2mm, the number of voxels in the model is set to 512×512×512, the number of pixels in the detector panel is set to 1024×1024, the projection sampling angle interval is 0.5°, the forward projection algorithm model used is the ray-driven projection model, and the ray step size is set to 1 voxel; use the full-angle projection data Projection of the hydrogen cylinder to be reconstructed conpeletedIterative reconstruction is performed, and the initial iterative value is directly using Projection limited For the result of FDK reconstruction, in each iteration, geometric constraints are used to limit and correct the iterative result;

[0082] The improved iterative algorithm formula is as follows:

[0083]

[0084] where λ k is the constraint factor λ k , which is used to constrain the update of data during the iteration: when x k ∈L, λ k =1, otherwise λ k =0.

[0085] The maximum number of iterations is set to 500. After the iteration is completed, the three-dimensional reconstructed image of the hydrogen cylinder to be measured is output.

[0086] In order to verify the effect of a finite-angle CT iterative reconstruction algorithm based on geometric feature constraints disclosed in the present invention, comparative experiments are carried out using hydrogen cylinder data. Figure 2 The following are the comparison graph of the reconstruction effect and the intermediate result graph of the present invention under finite-angle scanning and the FDK reconstruction effect on hydrogen cylinder data. Among them, (A) is the sinogram of the finite-angle projection of the standard hydrogen cylinder, (B) is the sinogram of the full-angle projection of the standard hydrogen cylinder, and (C) is the result of FBP reconstruction using (B). (D) is the sinogram of the finite-angle projection of the hydrogen cylinder with defects, (G) is the sinogram of the finite-angle projection of the defects obtained in step 2, (H) is the full-angle projection sinogram of the complemented defects obtained in steps 3 and 4, (E) is the full-angle projection sinogram of the complemented hydrogen cylinder with defects obtained in step 5, and (I) is the slice of the three-dimensional reconstructed image of the hydrogen cylinder with defects obtained in step 6. (F) is the reconstructed image of the hydrogen cylinder obtained by directly performing FBP reconstruction on (D). The Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) results are selected as shown Figure 3 It can be seen that after being processed by this method, the PSNR and SSIM of the finite-angle CT image of the hydrogen cylinder processed by the present invention are significantly improved.

[0087] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and retouches can be made, and these improvements and retouches all fall within the protection scope of the claims of the present invention.

Claims

1. A finite-angle CT iterative reconstruction algorithm based on geometric feature constraints, characterized in that: Including the following steps: S1: Calculate the geometric profile constraint condition L of this type of workpiece from the 0-360° complete angle CT scan projection data Projection of a standard and defect-free workpiece std Calculate the geometric profile constraint condition L of this type of workpiece; S2: CT scan projection data Projection of the workpiece to be measured at an angle of 0 to 120° llimited Perform data preprocessing through Projection std and Projection limited to obtain the limited-angle projection Projection of possible defects in the workpiece to be measured through the operation between them defects ; S3: Use the limited-angle projection of the defect Projection defects Perform iterative reconstruction to obtain the three-dimensional reconstructed image of the defect Data defects ; S4: Perform full-angle projection on the defective three-dimensional reconstruction image Data defects and combine it with the actual defective limited-angle projection Projection defects to obtain the completed full-angle projection Projection of the defect defects-conpeleted ; S5: The full-angle projection Projection after defect filling defects-conpeleted and the standard projection Projection of the workpiece std are operated to obtain the full-angle projection data Projection of the workpiece to be measured after defect filling conpeleted ; S6: Use Projection conpeleted Perform iterative reconstruction. In each iteration, use the geometric profile constraint L of this type of workpiece to restrict and correct the iterative result to obtain the three-dimensional reconstruction image Data of the workpiece to be measured recon .

2. The finite-angle CT iterative reconstruction algorithm based on geometric feature constraints according to claim 1, wherein: The specific steps of step S1 are as follows: S1.1: Perform data normalization on the 0-360° complete angle CT scan projection data Projection of a standard and defect-free workpiece std Specifically, when the sampling angle interval is θ, Projection std contains the projection data x of the standard workpiece at T = 360° / θ different angles k , k = 0, 1, 2, 3…, T-1; where the projection data x at each angle k is a two-dimensional matrix of shape H×W, where H and W are the sizes of the detection plate; for any point k in any x i,j,k , i ∈ [0, H-1], j ∈ [0, W-1], k ∈ [0, T-1], calculate the minimum value V min = Min(point i,j,k ), and the maximum value V max = Max(point i,j,k ); then perform normalization using the following formula: S1.2: Use the standard projection data Projection std Perform FDK reconstruction to obtain the three-dimensional data Data of this type of workpiece std , and the cone-beam CT geometric model parameters used in the FDK reconstruction process are consistent with the data source; S1.3: Manually select the workpiece geometric contour constraint condition L from the three-dimensional data Data of this type of workpiece. In order to make L fully cover the workpiece and at the same time maintain the binding force of L on the subsequent iterative reconstruction process, L is appropriately expanded outward on the basis of the actual geometric contour of the workpiece. std Among them, manually select the workpiece geometric contour constraint condition L from the three-dimensional data Data of this type of workpiece. In order to make L fully cover the workpiece and at the same time maintain the binding force of L on the subsequent iterative reconstruction process, L is appropriately expanded outward on the basis of the actual geometric contour of the workpiece.

3. A limited-angle CT iterative reconstruction algorithm based on geometric feature constraints according to claim 1, characterized in that: The specific steps of step S2 are as follows: S2: Extract the CT scan projection data from 0° to 120° from the standard projection data Projection std as the limited-angle standard projection Projection std2 , Projection std2 contains the standard workpiece projection data x at T / 3 different angles i , i = 0, 1, 2, 3…, T / 3 - 1, where T depends on the CT scan sampling interval, and the CT scan projection data Projection of the workpiece to be measured from 0° to 120° limited contains the projection data y of the workpiece to be measured at T / 3 different angles i , i = 0, 1, 2, 3…, T / 3 - 1; where the projection data x i or y i is a two-dimensional matrix of shape H×W, where H and W are the sizes of the detection board. Let y i subtract the corresponding point data value from x i to obtain z i = y i - x i , i = 0, 1, 2, 3…, T / 3 - 1, and the combination of z i results in the defective limited-angle projection Projection defects , and then perform normalization on Projection defects using the same normalization method as in S1.

1.

4. A limited-angle CT iterative reconstruction algorithm based on geometric feature constraints according to claim 1, characterized in that: The specific steps of step S3 are as follows: S3.1: Project the defect with limited angles, Projection defects The projection data z at different angles in i , i = 0, 1, 2, 3…, T / 3 - 1, is divided into 10 subsets according to the projection angles. The division method is as follows: Subset Set1 = {z i | i = 0, 10, 20, 30,…, T / 3 - 10}, Subset Set2 = {z i | i = 1, 11, 21, 31,…, T / 3 - 9}, Subset Set3 = {z i | i = 2, 12, 22, 32,…, T / 3 - 8}, Subset Set 10 = {z i | i = 9, 19, 29, 39,…, T / 3 - 1}; S3.2: Use the ordered subset expectation maximization (OS-EM) algorithm for reconstruction. Given an initial reconstructed image, set the number of subsets of the OS-EM algorithm to 10 and set the maximum number of iterations. For each iteration, sequentially access each subset in order. For each subset, perform the following operations: Based on the current reconstructed image, calculate the expected value of the data corresponding to this subset; update the reconstructed image according to the difference between this expected value and the actual measured value, and adjust the reconstructed image by minimizing the error. When the set maximum number of iterations is reached, the iteration is completed and the finally reconstructed image is output; The iterative reconstruction algorithm used is as follows: Among them, represents the value of the k-th pixel point in the n-th iteration (i.e., the current estimate of the reconstructed image), and this value will be updated according to the projection data and the reconstruction process in each iteration, and finally converge to the estimated value of the real image; represents the updated value of the k-th pixel point in the (n + 1)-th iteration, which is calculated from the previous iteration value and a factor adjusted through the expectation-maximization step; A ik is an element of the projection matrix, representing the contribution from the k-th pixel to the i-th projection data, calculated by a ray passing through the pixel point; p i is the i-th projection data, which is the projection intensity collected from the CT scanner. Each projection data corresponds to the measurement value of the CT scanner at different angles and reflects the projection from the scanning angle i to the target object. (Ax (n) ) i is the difference between the projection result of the reconstructed image after the n-th iteration and the true projection data p i and is used to calculate how to adjust the reconstructed image to make it closer to the true data; is the sum of all projection data, representing the total contribution of the k-th pixel to all projections, which is used to normalize the update factor to ensure that the update amplitude of each pixel is neither too large nor too small; p i / (Ax (n) ) i is the ratio of the projection data p i to the projection value (Ax (n) ) i obtained from the current reconstructed image through the projection matrix, representing the difference between the current reconstructed image and the true projection data.

5. A limited-angle CT iterative reconstruction algorithm based on geometric feature constraints according to claim 1, characterized in that: The specific steps of step S4 are as follows: S4.1: Perform full-angle projection on the defect three-dimensional reconstruction image Data defects and use the cone-beam CT geometric model parameters to be consistent with the data source device, and finally obtain T projection data; S4.2: The full-angle projection of the defects obtained in the previous step contains projection data F from 0° to 360° i , i = 0, 1, 2, 3…, T - 1, while the actual limited-angle projection of the defects, Projection defects contains projection data G from 0° to 120° i , i = 0, 1, 2, 3…, T / 3 - 1; Use the full-angle projection data of the defects to complement the actual limited-angle projection data of the defects to obtain the complemented full-angle projection data of the defects, Projection defects-conpeleted , Projection defects-conpeleted contains projection data H from 0° to 360° i , i = 0, 1, 2, 3…, T - 1, H i The calculation formula is as follows: When i ∈ [0, T / 3 - 1], H i = G i , when i ∈ [T / 3, T - 1], H i = F i .

6. The finite-angle CT iterative reconstruction algorithm based on geometric feature constraints according to claim 1, wherein: The specific steps of step S5 are as follows: S5.1: The fully - complemented full - angle projection data Projection of the defect defects-conpeleted Contains projection data H from 0 to 360° i , i = 0, 1, 2, 3…, T - 1, the standard projection Projection of the workpiece std Contains projection data J from 0 to 360° i , i = 0, 1, 2, 3…, T - 1, the fully - complemented full - angle projection data Projection of the workpiece to be measured is obtained through the operation between the two conpeleted , Projection conpeleted Contains projection data L from 0 to 360° i , i = 0, 1, 2, 3…, T - 1, the calculation method is as follows: L i = H i + J i , i = 0, 1, 2, 3…, T - 1; the two - dimensional matrix L i Is obtained by adding the corresponding elements of J i And H i ​ S5.2: Normalize L i , where i = 0, 1, 2, 3…, T-1, using the same normalization method as in S1.

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7. A limited-angle CT iterative reconstruction algorithm based on geometric feature constraints according to claim 1, characterized in that: The specific steps of step S6 are as follows: S6.1: The full-angle projection data Projection after supplementing the workpiece to be reconstructed conpeleted The projection data x at different angles in i , i = 0, 1, 2, 3…, T / 3 - 1, is divided into 10 subsets according to the projection angle, and the division method is as follows: Subset Set1 = {x i | i = 0, 10, 20, 30,…, T / 3 - 10}; Subset Set2 = {x i | i = 1, 11, 21, 31,…, T / 3 - 9}, Subset Set3 = {x i | i = 2, 12, 22, 32,…, T / 3 - 8}, Subset Set 10 = {x i | i = 9, 19, 29, 39,…, T / 3 - 1}; S6.2: Use the constrained OS-EM algorithm and the full-angle projection data Projection after the workpiece to be measured is completed for iterative reconstruction. The initial iteration value is directly Projection conpeleted for FDK reconstruction. In each iteration, use geometric constraints to limit and correct the iteration result; limited The result of FDK reconstruction is used. In each iteration, the iteration result is restricted and corrected using geometric constraints; The formula of the improved iterative algorithm is as follows: Among them, λ k is a constraint factor used to constrain the update of data during the iteration process: when x k ∈L, λ k = 1; otherwise, λ k = 0. After reaching the set maximum number of iterations, the final three-dimensional reconstructed image of the workpiece to be measured is obtained.

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