Limited-angle C-arm CT multi-objective optimization image reconstruction method based on image quality evaluation criteria

Abstract

The present application relates to a kind of limited angle C-arm CT multi-objective optimization image reconstruction method based on image quality evaluation standard, belong to the field of image reconstruction, comprising the following steps: S1: the ray source and area array detector are placed respectively in the center of the two sides of the to-be-detected, make the ray source and detector rotate limited angle along the orbit around the center of the to-be-detected to obtain incomplete projection data, then transmit to the storage in control and image processing system;S2: according to CT image reconstruction principle and projection data, establish multi-objective optimization model;S3: introduce image quality evaluation standard and simulated annealing algorithm to guide solving multi-objective optimization model, gradient descent method, L0 minimization method and guided filter method are used to solve multi-objective optimization model;S4: iteration step S3, until meeting output condition, output reconstructed image.

Description

Technical Field

[0001] This invention belongs to the field of image reconstruction and relates to a multi-objective optimized image reconstruction method for finite-angle C-arm CT based on image quality evaluation standards. Background Technology

[0002] In recent decades, X-ray computed tomography (CT) has been widely used in industrial inspection and clinical medicine. When the data acquired by the detector is complete, the filtered back projection (FBP) algorithm can reconstruct high-quality images. However, in some applications, such as breast CT, C-arm CT, and dental CT, data can only be acquired at limited scanning angles, resulting in incomplete data. For the reconstruction of limited-angle C-arm CT images, the FBP algorithm produces images with significant slippage artifacts. Furthermore, due to insufficient projection data, most image reconstruction algorithms result in the loss of edge structure and detail information. Therefore, improving the quality of reconstructed images from limited-angle C-arm CT, even with incomplete data, to meet non-destructive testing standards is of great practical significance.

[0003] In existing technologies, traditional algebraic reconstruction algorithms include Algebraic Reconstruction Technique (ART) and Simultaneous Algebraic Reconstruction Technique (SART). These algorithms primarily seek the least-squares solution of the discrete X-ray CT imaging model Af = P. However, traditional algebraic reconstruction algorithms are susceptible to noise interference. When the acquired projection data is incomplete, CT reconstruction is a typical inverse problem. Therefore, to mitigate the ill-posedness of this inverse problem, regularization strategies are often used, incorporating prior image information as constraints to construct a new objective function. For example, the TV (Total Variation)-based reconstruction algorithm introduces a regularization term. The TV algorithm has achieved good results in handling sparse-angle CT reconstruction, but for finite-angle C-arm CT reconstruction, this method suffers from over-smoothing of the image, and its performance in suppressing artifacts and protecting boundary structures is not very good for scans at smaller angles. Currently, Chen Zhiqiang has proposed a finite-angle C-arm CT reconstruction algorithm based on anisotropic TV. This algorithm incorporates prior information about the scanning range into the reconstruction process and considers its anisotropy at the same time. Therefore, this method can reconstruct higher quality images compared to TV.

[0004] Patent application CN 110717956A discloses "A Finite-Angle Projection Superpixel-Guided L0 Norm Optimization Reconstruction Method." This method first establishes an optimization objective equation based on a finite-angle projection dataset, then initializes parameters, iteratively reconstructs the image using the SARTA algorithm, and performs SLIC (Simple Linear Iterative Cluster) superpixel segmentation. Next, it solves for structural similarity and smoothing parameters on the segmented image, and applies a logarithmic transformation to obtain a higher-quality image. Then, it minimizes the gradient L0 norm of this higher-quality image to further improve image quality. Finally, it updates the image and repeats the iteration until convergence is met. While the method described in the patent application can effectively restore the CT image contour and reduce finite-angle artifacts, thereby improving the imaging quality and applicability of finite-angle C-arm CT, it still has the following drawback: the patent only considers optimizing one objective function first during the optimization process, meaning it does not consider that when optimizing another objective function, the image gradient L0 constraint may cause the image to become too smooth, leading to a decrease in image quality.

[0005] Patent application CN 115311379A discloses "A Finite CT Image Reconstruction Algorithm Based on Repair Matrix". This method first constructs a repair matrix based on prior information. Then, it updates the landslide artifact image using the repair matrix and a first preset auxiliary variable, and updates the reconstructed image using a system matrix and a second preset auxiliary variable. Next, it obtains a first update auxiliary variable based on the updated landslide artifact image and the first preset auxiliary variable, and a second update auxiliary variable based on the updated reconstructed image and the second preset auxiliary variable. Finally, it iterates until the iteration termination condition is met. While the method described in the patent application can repair the blurred and degraded details and edge information in the image caused by landslide artifacts, improving the quality of finite angle C-arm CT images, it still has the following drawback: updating the landslide artifact using the l0 norm does not consider the image gradient L0 constraint, which can lead to an overly smooth image and loss of image details.

[0006] Patent application CN 112529980A discloses "A Multi-Objective Finite-Angle C-Arm CT Image Reconstruction Method Based on Minimization." This method first establishes a multi-objective finite-angle C-arm CT image reconstruction model based on projection data and L0 sparse regularization constraints on the coefficients of the non-subsampled contourlet transform. Finally, it uses a minimization method to transform the reconstruction model into a single-objective optimization model for iterative reconstruction of the finite-angle C-arm CT image until the iteration conditions are met, at which point the image is output. While the method described in the patent application effectively suppresses artifacts and noise in the reconstructed image and protects image boundaries, thereby improving the quality of the CT reconstructed image, it still has the following drawback: in the process of optimizing the multi-objective function, the multi-objective optimization model is transformed into a single-objective optimization model for image reconstruction using a minimization method, without considering the simultaneous optimization of two objective functions. This can lead to a decrease in image quality during the optimization process.

[0007] Patent application CN 115564648A discloses a "Method and Apparatus for Reconstructing X-ray Finite-Angle C-arm CT Images Based on Generalized Total Variation". This method first initializes an estimated image using a finite-angle C-arm CT scan dataset and an image reconstruction operator related to CT scan geometric parameters, obtaining an intermediate image. Next, it uses gradient sparsity to constrain the intermediate image, then updates the estimated image. Finally, it iteratively updates the estimated image until it meets the iteration requirements, at which point the estimated image is output. While this patent overcomes the boundary blurring problem in existing finite-angle C-arm CT image reconstruction algorithms and improves the quality of the reconstructed image, it still has the following drawbacks: the patent only considers using the sparsity of image gradients to constrain the intermediate image, uses only a single-objective optimization method to optimize this index, and artifact suppression only considers artifacts in the x and y axes of the image, without considering the multi-scale nature of image artifacts.

[0008] Most existing optimization and reconstruction methods, although considering multiple image metrics, only use single-objective optimization methods to optimize that metric. After optimizing one objective, they then optimize another. Although the objective function value is relatively small, it may lead to a deterioration in image quality during the optimization process, with artifacts and broken edges in the reconstructed image. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a finite-angle C-arm CT multi-objective optimization image reconstruction method based on image quality evaluation criteria, which avoids image quality degradation when optimizing multi-objective functions, and introduces a simulated annealing algorithm to avoid getting trapped in local minima during the optimization process, thereby improving the quality of the reconstructed image to a greater extent.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A finite-angle C-arm CT multi-object optimization image reconstruction method based on image quality evaluation criteria includes the following steps:

[0012] S1: Acquire projection data: Place the X-ray source and the array detector on both sides of the center to be inspected, and rotate the X-ray source and the detector around the center along the track by a limited angle to obtain incomplete projection data, which is then transmitted to the control and image processing system for storage.

[0013] S2: Based on the principles of CT image reconstruction and projection data, establish a multi-objective optimization model;

[0014] S3: Iterative Reconstruction of C-arm CT with Finite Angle: Using structural similarity image quality evaluation criteria and simulated annealing algorithm to guide the solution of multi-objective optimization model, and employing gradient descent method, L0 minimization method and guided filtering method to solve the multi-objective optimization model;

[0015] S4: Repeat step S3 iteratively until the output condition is met, and output the reconstructed image.

[0016] Furthermore, the multi-objective optimization model described in step S2 is as follows:

[0017]

[0018] Where A represents the system projection matrix, f represents the pixel value, and g δ Let D represent noisy projected data, where D is a diagonal matrix and #{} denotes a counting operator. This represents the number of non-zero terms that satisfy the condition, where Let l0 be the gradient of the image; the gradient of the image at (i′,j′) is represented as

[0019] Furthermore, the finite-angle C-arm CT iterative reconstruction process described in step S3 is as follows:

[0020] S31: First, solve the following subproblem using gradient descent and convex set projection algorithms:

[0021]

[0022] A preliminary solution is obtained:

[0023]

[0024] Where f (k+1 ) represents the solution obtained after the (k+1)th iteration, f (k ) represents the solution obtained in the k-th iteration, and U has diagonal elements of . a diagonal matrix;

[0025] S32: The image quality metric SSIM and simulated annealing algorithm are introduced to guide the optimization process. When the image quality deteriorates, the optimization process stops iterating.

[0026] For a given reference image I, if the iteration point f (k+1) The SSIM value between the given image I and the SSIM(f) (k +1) I) is greater than the iteration point f (k) The SSIM value between the given image I and the SSIM(f) (k) If I), then repeat the iterative process (3); otherwise, accept the solution in the form of probability.

[0027]

[0028] Where ΔE = SSIM(f (k) ,I)-SSIM(f (k+1) ,I), T1 is the temperature parameter of the simulated annealing algorithm;

[0029] If we accept f (k+1 Continue the iterative process (3) and repeat it; otherwise, f (k) As the input image, f (k+1 Using the guided image as a guide image, the Guided Image Filtering (GIF) method is employed. (k+1) =GIF(f (k) ,f (k+1 Generate a new iterative image;

[0030] S33: The solution from step S32 is added as a constraint to the first objective optimization, as shown below:

[0031]

[0032] Among them, the nearest neighbor operator is used to solve the optimization problem (8), as shown below:

[0033]

[0034] The optimization problem is solved using the L0 minimization method (9);

[0035] S34: The image quality metric SSIM and the simulated annealing algorithm SA are introduced to guide the optimization process. The optimization iteration process stops when the image quality deteriorates. For a given image I, if SSIM(f (k+2) ,I)>SSIM(f (k+1 If I), then the iterative process is repeated; otherwise, in order to exceed the local extremum, this invention will accept points of the following probabilistic form:

[0036]

[0037] Where ΔE = SSIM(f (k+1 ),I)-SSIM(f (k+2) T2 is the temperature parameter in the simulated annealing algorithm;

[0038] If we accept f (k+2 If the iteration process is repeated, then a new iterative image f is generated using the guided image filtering method in step S32. (k+2) =GIF(f (k) ,f (k+2) ), and serve as the initial image for S31.

[0039] Furthermore, the guided image filtering method GIF described in step S32 is as follows:

[0040] S321: Given an input image I = f (k) and guiding image G=f (k+1) Assume that the filtered output q and the guided image G have a locally linear relationship, that is:

[0041]

[0042] Where, ω l The filtering window is centered on pixel l, a l b l The coefficients are linear.

[0043] To solve a l and b l Based on the above expression and the difference between q and the input image, GIF obtains the following function:

[0044]

[0045] Where ε is the regularization parameter, which penalizes excessively large values ​​of a. l ;

[0046] Solve for the filtering result, i.e., minimize E(a) i ,b l Therefore, for a respectively l and b l Differentiating, we get:

[0047]

[0048]

[0049] Where |ω| is the local filtering window ω l The number of pixels in The guide image and the input image are respectively in ω l The mean of the middle, Is the guiding image at ω l The variance in;

[0050] The average of the filtered outputs from different windows is used as the final filtered output. The formula for the final GIF is expressed as:

[0051]

[0052] Where q i It is the image output after guided filtering. They are a l and b l The average value.

[0053] Furthermore, step S33 specifically includes:

[0054] S331: Introducing two auxiliary variables h and v, the proximal endpoint operator problem is then transformed into the following:

[0055]

[0056] in

[0057] S332: Using the penalty function method, problem (10) is transformed into the following optimization problem:

[0058]

[0059] Where τ is the guarantee variable (h) i′,j′ ,v i′,j′ )near One of the parameters;

[0060] S333: Let l be the iteration index, and give the iteration format of optimization problem (11):

[0061]

[0062] S334: The exact minimum value of subproblem f is obtained by the diagonal derivative operator after Fast Fourier Transform, and the minimum value of subproblem (h,v) is obtained by the Hard Thresholding function. The iterative format (12) is rewritten as follows:

[0063]

[0064] The Fourier transform is denoted as F, and the inverse Fourier transform is denoted as Finverse. -1 , F() *Let F(1) denote the complex conjugate, and let F(1) denote the inverse Fourier transform of the increment function, and:

[0065]

[0066] remember Among them l max It represents the maximum number of iterations.

[0067] The beneficial effects of this invention are that the finite angle artifacts and noise of the reconstructed CT images after processing by this method can be effectively suppressed, and the boundaries can be effectively protected, thereby greatly improving the quality of the reconstructed images.

[0068] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0069] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0070] Figure 1 This is a schematic diagram of a limited-angle C-arm CT scan.

[0071] Figure 2 A multi-object optimized image reconstruction method for finite-angle C-arm CT based on image quality evaluation criteria;

[0072] Figure labels: 1. X-ray source; 2. Area array detector; 3. Center to be inspected; 4. Orbit. Detailed Implementation

[0073] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0074] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0075] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0076] Figure 1 This is a schematic diagram of the scanning structure of the limited-angle C-arm CT of the present invention. As shown in the figure: Before data acquisition, the X-ray source 1 and the area array detector 2 are placed on both sides of the center 3 to be inspected; during data acquisition, the X-ray source 1 rotates around the track 4 by a limited angle, and at the same time, the detector 2 rotates synchronously to obtain incomplete projection data; after the data is acquired, it is transmitted to the control and image processing system for storage.

[0077] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings; it should be understood that the preferred embodiments are only for illustrating the present invention and are not intended to limit the scope of protection of the present invention.

[0078] S1: Acquisition of projection data: Under the control of the control and image processing system, the X-ray source 1 and detector 2 are first rotated around the center to be inspected along the track 4 by a limited angle to obtain incomplete projection data, which is then transmitted to the control and image processing system 5 for storage.

[0079] S2: Establish a multi-objective optimization model

[0080] Based on the principles of CT image reconstruction and projection data, a multi-objective optimization model is established:

[0081]

[0082] Where D is a diagonal matrix, #{} denotes the counting operator, and ||β||0 represents... and The number of these two non-zero terms, among which Let l0 be the gradient of the image. The gradient of the image at (i′, j′)

[0083] S3: Iterative reconstruction of C-arm CT with limited angle: Based on the established model (1), the Structural Similarity (SSIM) image quality evaluation standard and Simulated Annealing (SA) algorithm are used to guide the solution of model (1);

[0084] The specific process of step S3, finite-angle C-arm CT iterative reconstruction, is as follows:

[0085] S31: First, solve the following subproblem using gradient descent and convex set projection algorithms:

[0086]

[0087] A preliminary solution is obtained:

[0088]

[0089] Where U is the diagonal element. A diagonal matrix.

[0090] S32: Secondly, the image quality metric SSIM and simulated annealing algorithm are introduced to guide the optimization process. The optimization iteration stops when the image quality deteriorates. For a given reference image I, if the iteration point f... (k+1) The SSIM value between the given image I and the image I (denoted as SSIM(f)) (k+1) I)) is greater than the iteration point f (k) The SSIM value between the given image I and the image I (denoted as SSIM(f)) (k) If I), then repeat the iterative process (3). Otherwise, we accept the solution in probabilistic form:

[0091]

[0092] Where ΔE = SSIM(f (k) ,I)-SSIM(f (k+1) ,I), T1 is the temperature parameter of the simulated annealing algorithm.

[0093] If we accept f (k+1) Continue the iterative process (3) repeatedly; otherwise, f (k) As input image and f (k+1) As a guide image, the Guided Image Filtering (GIF) method is used to... (k+1) =GIF(f (k) ,f(k+1) Generate a new iterative image.

[0094] The GIF illustrating the guided image filtering method is shown below:

[0095] Guided image filtering methods first give an input image I = f (k) and guiding image G=f (k+1) First, assume that the filtered output q and the guided image G have a locally linear relationship, that is: Where, ω l The filtering window is centered on pixel l, a l b l These are linear coefficients.

[0096] This local linear model ensures that the edges of the filtered output image correspond one-to-one with the edges of the guiding image, providing a basis for solving a. l and b l Based on the above expression and the difference between q and the input image, GIF obtains the following function:

[0097] Where ε is the regularization parameter, which penalizes excessively large values ​​of a. l Solve for the filtering result, i.e., minimize E(a). i ,b l Therefore, for a respectively l and b l Differentiation yields: Where |ω| is the local filtering window ω l The number of pixels in The guide image and the input image are respectively in ω l The mean of the middle, Is the guiding image at ω l The variance in.

[0098] The average of the filtered outputs from different windows is used as the final filtered output. Due to the symmetry of the windows, the final GIF is expressed as follows:

[0099] Where q i It is the image output after guided filtering. They are a l and b l The average value.

[0100] S33: Then, the solution from the previous step is added as a constraint to the first objective optimization, as shown below:

[0101]

[0102] Among them, the nearest neighbor operator is used to solve the optimization problem (8), as shown below:

[0103]

[0104] The optimization problem is solved using the L0 minimization method (9).

[0105] S331: First, introduce two auxiliary variables h and v, then the proximal endpoint operator problem is transformed into the following:

[0106]

[0107] in

[0108] S332: Secondly, using the penalty function method, problem (10) can be transformed into the following optimization problem:

[0109]

[0110] Where τ is the guarantee variable (h) i′,j′ ,v i′,j′ )near One of the parameters.

[0111] S333: Then, let l be the iteration index, then the iterative formula for the optimization problem (11) can be given by the following formula:

[0112]

[0113] S334: Finally, the exact minimum of subproblem f can be obtained by the diagonal derivative operator after Fast Fourier Transform, and the minimum of subproblem (h,v) can be obtained by the Hard Thresholding function. Therefore, the iterative format (12) can be rewritten as follows:

[0114]

[0115] The Fourier transform is denoted as F, and the inverse Fourier transform is denoted as Finverse. -1 , F() * Let F(1) denote the complex conjugate, and let F(1) denote the inverse Fourier transform of the increment function, and:

[0116]

[0117] remember Among them l max It represents the maximum number of iterations.

[0118] S34: Finally, to avoid When the image quality is extremely small, the image quality deteriorates. This invention still introduces the image quality metric SSIM and the simulated annealing algorithm SA to guide the optimization process. The optimization iteration process stops when the image quality deteriorates. For a given image I, if SSIM(f (k+2) ,I)>SSIM(f (k+1) If I), then repeat the iterative process (13); otherwise, in order to exceed the local extremum, the present invention will accept points in the following probabilistic form:

[0119]

[0120] Where ΔE = SSIM(f (k+1) ,I)-SSIM(f (k+2) ,I), T2 is the temperature parameter in the simulated annealing algorithm.

[0121] If we accept f (k+2 Continue the iterative process (13) repeatedly; otherwise, generate a new iterative image f using the guided image filtering method in S32 above. (k+2) =GIF(f (k) ,f (k+2) ), and serve as the initial image for S31.

[0122] S4: This invention repeats step S3 iteratively until the output conditions are met, and then outputs the reconstructed image.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A finite-angle C-arm CT multi-objective optimized image reconstruction method based on image quality evaluation criteria, characterized in that: Includes the following steps: S1: Acquire projection data: Place the X-ray source and the array detector on both sides of the center to be inspected, and rotate the X-ray source and the detector around the center along the track by a limited angle to obtain incomplete projection data, which is then transmitted to the control and image processing system for storage. S2: Based on the principles of CT image reconstruction and projection data, establish a multi-objective optimization model; S3: Finite-Angle C-Arm CT Iterative Reconstruction: Utilizing structural similarity image quality evaluation criteria and simulated annealing algorithm to guide the solution of a multi-objective optimization model, employing gradient descent method... The multi-objective optimization model is solved using minimization and guided filtering methods; the finite-angle C-arm CT iterative reconstruction process described in step S3 is as follows: S31: First, solve the following subproblem using gradient descent and convex set projection algorithms: (2) A preliminary solution is obtained: (3) in Indicates the first The solution obtained after the next iteration. Indicates the first The solution obtained in the second iteration. diagonal elements are a diagonal matrix; S32: The image quality metric SSIM and simulated annealing algorithm are introduced to guide the optimization process. When the image quality deteriorates, the optimization process stops iterating. For a given reference image If the iteration point and the given image SSIM values ​​between Greater than the iteration point and the given image SSIM values ​​between If the solution is positive, repeat the iteration process (3); otherwise, accept the solution in terms of probability. (4) in , These are the temperature parameters of the simulated annealing algorithm; If accepted Continue repeating the iteration process (3), otherwise, As input image GIF is used as a guide image for filtering purposes. Generate a new iterative image; S33: The solution from step S32 is added as a constraint to the first objective optimization, as shown below: (8) Among them, the nearest neighbor operator is used to solve the optimization problem (8), as shown below: (9) use The minimization method is used to solve the optimization problem (9); S34: The image quality metric SSIM and the simulated annealing algorithm SA are introduced to guide the optimization process. The optimization iteration process stops when the image quality deteriorates; for a given image... ,if If the iteration process is repeated, then the invention will continue; otherwise, in order to exceed the local extremum, the invention will accept points of the following probabilistic form: ，(14) in , These are the temperature parameters in the simulated annealing algorithm; If, accept Continue the iterative process; otherwise, generate a new iterative image using the guided image filtering method in step S32. And as the initial image of S31; S4: Repeat step S3 iteratively until the output condition is met, and output the reconstructed image.

2. The finite-angle C-arm CT multi-object optimized image reconstruction method based on image quality evaluation criteria according to claim 1, characterized in that: The multi-objective optimization model mentioned in step S2 is: ,(1) in, Represents the system projection matrix. Represents pixel value, This represents noisy projection data. It is a diagonal matrix. Represents a counting operator. This represents the number of non-zero terms that satisfy the condition, where For image Gradient; Image in The gradient is expressed as .

3. The finite-angle C-arm CT multi-object optimized image reconstruction method based on image quality evaluation criteria according to claim 1, characterized in that: The guided image filtering method described in step S32 is GIF: S321: Given an input image and guide image Assuming the filtered output and guide image They form a local linear relationship, that is: in, It is based on pixels The center of the filtering window, , The coefficients are linear. To solve and GIF introduces based on the above expression. The difference between the input image and the output image yields the following function: in It's a regularization parameter that penalizes excessively large values. ; Solve for the filtering result, i.e. minimize Therefore, respectively for and Differentiating, we get: in Local filtering window The number of pixels in , The guide image and the input image are respectively in The mean of the middle, Is the guiding image in The variance in; The average of the filtered outputs from different windows is used as the final filtered output. The formula for the final GIF is expressed as: in It is the image output after guided filtering. , They are and The average value.

4. The finite-angle C-arm CT multi-object optimized image reconstruction method based on image quality evaluation criteria according to claim 1, characterized in that: Step S33 specifically includes: S331: Introduce two auxiliary variables and Then the proximal endpoint operator problem is transformed into the following: (10) in ; S332: Using the penalty function method, problem (10) is transformed into the following optimization problem: (11) in It is to guarantee variables near One of the parameters; S333: Let For the iterative index, the iterative format of optimization problem (11) is given: (12) S334: Obtaining the subproblem through the diagonal derivative operator after the Fast Fourier Transform. The exact minimum value is obtained through a hard threshold function. The minimum value is obtained by rewriting the iteration format (12) as follows: (13) The Fourier transform is denoted as... The inverse Fourier transform is denoted as , Indicates complex conjugation. Let represent the inverse Fourier transform of the increment function, and: remember ,in It represents the maximum number of iterations.

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