CT image reconstruction method and system based on ridge regression and detail conduction

Abstract

The invention discloses a ridge regression and detail conduction-based CT image reconstruction method and system, and belongs to the technical field of CT image reconstruction, and the method comprises the steps: constructing a mask, and carrying out the fusion of an FBP reconstruction image filtering result and an SART reconstruction image filtering result through the mask, and obtaining a guide image; calculating detail information of the FBP reconstructed image, capturing local detail change of the FBP reconstructed image, and obtaining a detail layer result of the FBP reconstructed image; combining the calculated detail layer result of the FBP reconstructed image with the filtering result of the FBP reconstructed image, fusing the mask with the filtering result of the SART reconstructed image to obtain a final image, and filtering the filtering result of the SART reconstructed image by taking the final image as a guide image to obtain an initial value of SART iteration; and enabling the initial value of the SART iteration to participate in a SART reconstruction process for iteration until a final reconstructed image is obtained. According to the method, the inherent limitation of SART in the aspect of keeping high-frequency information is effectively made up, stripe artifacts are reduced, and the overall quality and fidelity of a reconstructed image are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of CT image reconstruction, and particularly relates to a CT image reconstruction method and system based on ridge regression and detail conduction. Background Art

[0002] Currently, using sparse-angle or noisy projection data to reconstruct high-quality computed tomography (CT) images is an important research direction in current scientific research work.

[0003] At present, the analytical reconstruction method is vulnerable to noise in the sparse-angle scenario, but can retain the high-frequency edges and texture details of the object; while iterative reconstruction methods such as SART (Simultaneous Algebraic Reconstruction Technique), although they can combine prior information and constraints to generate high-quality images and improve the reconstruction accuracy, mainly recover low-frequency information in the initial iteration process, and the high-frequency details are recovered relatively late. It can be seen that traditional reconstruction algorithms are difficult to effectively retain fine details while reducing streak artifacts when dealing with sparse-angle or noisy projection data, and cannot meet the requirements for high-quality CT image reconstruction. Summary of the Invention

[0004] Therefore, the present invention provides a CT image reconstruction method and system based on ridge regression and detail conduction, which solves the problem that traditional technologies are difficult to balance reducing streak artifacts and retaining fine details when dealing with sparse-angle or noisy projection data.

[0005] To achieve the above object, the present invention provides the following technical solution: A CT image reconstruction method based on ridge regression and detail conduction, comprising:

[0006] Performing FBP reconstruction and SART reconstruction on the projection data respectively to obtain an FBP reconstructed image and an SART reconstructed image, and respectively performing guided image filtering based on ridge regression on the FBP reconstructed image and the SART reconstructed image to obtain an FBP reconstructed image filtering result and an SART reconstructed image filtering result;

[0007] Constructing a mask, and fusing the FBP reconstructed image filtering result and the SART reconstructed image filtering result through the mask to obtain a guided image;

[0008] Calculating the detail information of the FBP reconstructed image, capturing the local detail changes of the FBP reconstructed image, and obtaining a detail layer result of the FBP reconstructed image;

[0009] Combine the detail layer result of the calculated FBP reconstructed image with the filtered result of the FBP reconstructed image, and fuse the mask with the filtered result of the SART reconstructed image to obtain the final image. Use the final image as the guiding image to filter the filtered result of the SART reconstructed image to obtain the initial value of the SART iteration;

[0010] Let the initial value of the SART iteration participate in the SART reconstruction process for iteration until the final reconstructed image is obtained.

[0011] As a preferred solution of the CT image reconstruction method based on ridge regression and detail conduction, in the guided image filtering based on ridge regression, the filtered output object is the linear transformation of the guiding image in a square window centered on the pixel, and the linear coefficient is determined by minimizing the cost function containing the regularization parameter.

[0012] As a preferred solution of the CT image reconstruction method based on ridge regression and detail conduction, in the process of constructing the mask:

[0013] Calculate the difference between the linearized data of the filtered result of the FBP reconstructed image and the filtered result of the SART reconstructed image, compare the difference of the linearized data with the set threshold, and determine the mask value according to the comparison result.

[0014] As a preferred solution of the CT image reconstruction method based on ridge regression and detail conduction, in the process of calculating the detail information of the FBP reconstructed image, add the parameter ε to both the numerator and denominator of the formula for calculating the detail information of the FBP reconstructed image, and use the parameter ε to avoid transmitting noise and the situation of being divided by zero;

[0015] Calculate the detail information F of the FBP reconstructed image Detail The formula is:

[0016]

[0017] In the formula, F represents the FBP reconstructed image, and F GIF is the guided image filtering result of F.

[0018] As a preferred solution of the CT image reconstruction method based on ridge regression and detail conduction, the formula for letting the initial value of the SART iteration participate in the SART reconstruction process for iteration is:

[0019]

[0020] The relaxation coefficient λ K Satisfies:

[0021] 0 ≤ ε ≤ λ K ≤ (2 - ε) / max{W i ∣ i = 1, 2, …, M}

[0022]

[0023] In the formula, is the formula after iteration, is the formula before iteration; K = 0, 1…, λ K > 0 is the relaxation coefficient; a ij is the contribution of the j-th pixel to the i-th X-ray; p i is the projection data collected by the detector; is the linear attenuation coefficient of the n-th pixel of the object to be measured at the K-th iteration; M and N are the orders of positive definite diagonal matrices.

[0024] The present invention also provides a CT image reconstruction system based on ridge regression and detail conduction, including:

[0025] A projection data reconstruction module for respectively performing FBP reconstruction and SART reconstruction on the projection data to obtain an FBP reconstructed image and an SART reconstructed image;

[0026] A guided image filtering module for respectively performing guided image filtering based on ridge regression on the FBP reconstructed image and the SART reconstructed image to obtain an FBP reconstructed image filtering result and an SART reconstructed image filtering result;

[0027] A guided image reconstruction module for constructing a mask and fusing the FBP reconstructed image filtering result and the SART reconstructed image filtering result through the mask to obtain a guided image;

[0028] A detail layer analysis module for calculating the detail information of the FBP reconstructed image, capturing the local detail changes of the FBP reconstructed image, and obtaining a detail layer result of the FBP reconstructed image;

[0029] A final image generation module for combining the calculated detail layer result of the FBP reconstructed image with the FBP reconstructed image filtering result, and fusing the mask with the SART reconstructed image filtering result to obtain a final image;

[0030] An initial value generation module for filtering the SART reconstructed image filtering result with the final image as a guided image to obtain an initial value for SART iteration;

[0031] An iterative reconstruction module for participating the initial value of the SART iteration in the SART reconstruction process for iteration until a final reconstructed image is obtained.

[0032] As an optimal solution of the CT image reconstruction system based on ridge regression and detail conduction, in the guided image filtering module, the filtered output object is the linear transformation of the guided image in a square window centered on the pixel, and the linear coefficients are determined by minimizing the cost function containing the regularization parameter.

[0033] As an optimal solution of the CT image reconstruction system based on ridge regression and detail conduction, in the guided image reconstruction module:

[0034] Calculate the difference between the linearized data of the filtered results of the FBP reconstructed image and the filtered results of the SART reconstructed image, compare the difference of the linearized data with the set threshold, and determine the mask value according to the comparison result.

[0035] As an optimal solution of the CT image reconstruction system based on ridge regression and detail conduction, in the detail layer analysis module, add the parameter ε to both the numerator and denominator of the formula for calculating the detail information of the FBP reconstructed image, and avoid transmitting noise and the situation of division by zero through the parameter ε;

[0036] Calculate the detail information F of the FBP reconstructed image Detail The formula is:

[0037]

[0038] In the formula, F represents the FBP reconstructed image, and F GIF is the filtered result of the guided image of F.

[0039] As an optimal solution of the CT image reconstruction system based on ridge regression and detail conduction, in the iterative reconstruction module, the formula for iterating the initial value of the SART iteration in the SART reconstruction process is:

[0040]

[0041] The relaxation coefficient λ K satisfies:

[0042] 0 ≤ ε ≤ λ K ≤ (2 - ε) / max{W i ∣ i = 1, 2, …, M}

[0043]

[0044] In the formula, is the formula after iteration, is the formula before iteration; K = 0, 1 …, λ K > 0, is the relaxation coefficient; a ij is the contribution of the jth pixel to the ith X-ray; p i is the projection data collected by the detector; is the linear attenuation coefficient of the nth pixel of the object under test at the Kth iteration; M and N are the orders of positive definite diagonal matrices.

[0045] The beneficial effects of the present invention are as follows. The projection data are respectively subjected to FBP reconstruction and SART reconstruction to obtain an FBP reconstruction image and an SART reconstruction image. The FBP reconstruction image and the SART reconstruction image are respectively subjected to guided image filtering based on ridge regression to obtain an FBP reconstruction image filtering result and an SART reconstruction image filtering result; a mask is constructed, and the FBP reconstruction image filtering result and the SART reconstruction image filtering result are fused through the mask to obtain a guided image; the detail information of the FBP reconstruction image is calculated to capture the local detail changes of the FBP reconstruction image, and a detail layer result of the FBP reconstruction image is obtained; the calculated detail layer result of the FBP reconstruction image is combined with the FBP reconstruction image filtering result, and the mask is fused with the SART reconstruction image filtering result to obtain a final image. The final image is used as a guided image to filter the SART reconstruction image filtering result to obtain an initial value for SART iteration; the initial value of the SART iteration participates in the SART reconstruction process for iteration until a final reconstruction image is obtained. The present invention effectively makes up for the inherent limitation of SART in retaining high-frequency information, not only reduces streak artifacts, but also improves the overall quality and fidelity of the reconstructed image. The experimental results of simulated data and real data prove the effectiveness of the SART-DT algorithm in generating high-quality reconstructions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and for those of ordinary skill in the art, other implementation drawings can be obtained according to the provided drawings without creative efforts.

[0047] The structures, proportions, sizes, etc. shown in this specification are only used to cooperate with the content disclosed in the specification for those who are familiar with this technology to understand and read, and are not used to limit the limiting conditions under which the present invention can be implemented. Therefore, they do not have technical substance. Any modification of the structure, change of the proportional relationship or adjustment of the size should still fall within the scope covered by the technical content disclosed in the present invention without affecting the effects that the present invention can produce and the purposes that can be achieved.

[0048] Figure 1 is a schematic flowchart of a CT image reconstruction method based on ridge regression and detail conduction provided by an embodiment of the present invention;

[0049] Figure 2Differences between the Gaussian low-pass filter and GIF provided in the embodiments of the present invention when processing image edges;

[0050] Figure 3 Flowchart of the SART-DT algorithm provided in the embodiments of the present invention;

[0051] Figure 4 Reconstruction results of the simulated projection data under different reconstruction methods provided in the embodiments of the present invention;

[0052] Figure 5 Relative error curves of the results of each reconstruction method in each iteration and GT in the simulation experiment provided in the embodiments of the present invention;

[0053] Figure 6 Reconstruction results of the real projection data under different reconstruction methods provided in the embodiments of the present invention;

[0054] Figure 7 Relative error curves of the results of each reconstruction method and GT in the real experiment provided in the embodiments of the present invention;

[0055] Figure 8 Comparison of the pixel values of each reconstruction method at the line drawing position provided in the embodiments of the present invention;

[0056] Figure 9 Schematic diagram of the CT image reconstruction system architecture based on ridge regression and detail conduction provided in the embodiments of the present invention. Detailed implementation manners

[0057] The following specific embodiments illustrate the implementation manners 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. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0058] Embodiment 1

[0059] As is well known, Guided image filtering (GIF) is a local linear filter with good edge preservation characteristics and low time complexity. In GIF, the filtered output f GIF is a linear transformation of the guidance image I in a square window ω n centered at pixel n with a radius of r:

[0060]

[0061] where i is the pixel index. (a n,b n ) is ω n The linear coefficient assumed to be constant in ω n has a size of 3×3. (a n ,b n ) is determined by minimizing the following cost function in ω n :

[0062]

[0063] The above equation represents a linear ridge regression model, where f i is the filtered input of the image f at pixel i. ε is a regularization parameter used to penalize large a n values to prevent overfitting or instability of the model. Its solution can be represented by linear regression:

[0064]

[0065] In the equation, μ n and σ n 2 are the mean and variance of the guidance image I in ω n respectively. is the average value of the input image f in ω n . |ω| is the number of pixels in ω n . If the guidance image I is set to the filtered input image f, we can obtain:

[0066]

[0067] b n =(1 - a n )μ n

[0068] Since a given pixel i is involved in multiple windows, the value of f i GIF is different when calculated in different windows. A simple strategy is to average all the values of f i GIF . After calculating (a n ,b n ) for all windows, the output of the filter can be calculated as:

[0069]

[0070] In the equation, and are the average coefficients calculated from all overlapping windows.

[0071] As is well known, a CT imaging system can be modeled as:

[0072] Af = p

[0073] where A = (a ij ) represents an M×N measurement matrix, a ij is the contribution of the jth pixel to the ith X-ray, p is the projection data collected by the detector, and f ∈ R N is the linear attenuation coefficient of the object to be measured. The task of CT imaging is to reconstruct f from p. The convergence of the following simultaneous iteration scheme is considered:

[0074] f (K+1) = f (K) + λ K V -1 A * W(p - Af (K) )

[0075] where K = 0, 1…, λ K > 0 is the relaxation coefficient, and V and W are two positive definite diagonal matrices of order N and M respectively. The SART algorithm is a special case of the formula f (K+1) = f (K) + λ K V -1 A * W(p - Af (K) ), and its formula can be expressed as:

[0076]

[0077] V and W are defined as follows respectively:

[0078] V = diag(V 1 , V 2 , …, V N )

[0079] W = diag(W 1 , W 2 , …, W M )

[0080] And there is:

[0081]

[0082]

[0083] Among them, the SART relaxation parameter λ is selected by considering the convergence theorem k : Assume that for all i = 1, 2,..., M, W i > 0, and for all K ≥ 0, if

[0084] 0 ≤ ε ≤ λ K ≤ (2 - ε) / max{W i∣i = 1, 2, …, M}

[0085] where ε is an arbitrarily small constant, then any sequence generated by SART converges to the weighted least squares solution f * = argmin{||Af - p|| 2 ∣f ∈ R n}}

[0086] The SART method can generate higher quality images and improve the reconstruction accuracy by combining prior information and constraints. In the initial iterative process of SART, mainly low-frequency information is recovered. This is because the initial iteration focuses on adjusting the overall structure and shape to match the projection data. As the number of iterations increases, the detailed information is gradually recovered, and high-frequency components such as edges and fine structures in the image become clearer. In view of the complementarity between the high-frequency information of the analytical reconstruction method and the low-frequency information of the iterative reconstruction method, the embodiments of the present invention propose a new reconstruction scheme that combines SART with detail transmission throughout the iterative process, thereby improving the quality of the final image, effectively reducing streak artifacts and retaining finer details. The following is the specific content of the embodiments of the present invention.

[0087] Referring to Figure 1 , Embodiment 1 of the present invention provides a CT image reconstruction method based on ridge regression and detail conduction, including the following steps:

[0088] S1. Perform FBP reconstruction and SART reconstruction on the projection data respectively to obtain an FBP reconstruction image and an SART reconstruction image, and perform guided image filtering based on ridge regression on the FBP reconstruction image and the SART reconstruction image respectively to obtain the FBP reconstruction image filtering result and the SART reconstruction image filtering result;

[0089] S2. Construct a mask, and fuse the FBP reconstruction image filtering result and the SART reconstruction image filtering result through the mask to obtain a guided image;

[0090] S3. Calculate the detail information of the FBP reconstruction image, capture the local detail changes of the FBP reconstruction image, and obtain the detail layer result of the FBP reconstruction image;

[0091] S4. Combine the calculated detail layer result of the FBP reconstruction image with the FBP reconstruction image filtering result, and fuse the mask with the SART reconstruction image filtering result to obtain a final image, and use the final image as a guided image to filter the SART reconstruction image filtering result to obtain the initial value of SART iteration;

[0092] S5. Participate the initial value of the SART iteration in the SART reconstruction process for iteration until the final reconstruction image is obtained.

[0093] In this embodiment, in step S1, in the guided image filtering based on ridge regression, the filtering output object is a linear transformation of the guided image in a square window centered on a pixel, and the linear coefficients are determined by minimizing a cost function including a regularization parameter.

[0094] Specifically, in order to generate a better initial value for SART iteration, a mask Μ is calculated, and the guided image D is obtained through the following formula:

[0095] D = (1 - Μ)·F GIF + Μ·f (K+1)GIF

[0096] In the formula, F represents the FBP (Filtered Back Projection) reconstructed image, and F GIF is the result of guided image filtering of F. For convenience, S is used to represent the SART reconstructed image, and S GIF is the result of guided image filtering of S, and S GIF i.e., f (K+1)GIF . In this way, Μ adjusts the relative contributions of information from different sources during the generation of the initial value, in order to obtain a better initial value, thereby improving the quality of the reconstructed image in the subsequent iterative reconstruction process. Among them, a threshold is added to calculate Μ by finding pixels with a smaller difference between F and S:

[0097]

[0098] In the formula, and are the linearizations of F GIF and S GIF respectively. The SART algorithm is used to iterate the initial value to obtain the final reconstructed image.

[0099] In this embodiment, in step S2, during the construction of the mask:

[0100] Calculate the difference between the linearized data of the filtering result of the FBP reconstructed image and the filtering result of the SART reconstructed image, compare the difference of the linearized data with a set threshold, and determine the mask value according to the comparison result. Although GIF can reduce noise, it cannot add the detailed information that may exist in the FBP reconstructed image. In order to transmit the detailed information, in step S3, during the calculation of the detailed information of the FBP reconstructed image, a parameter ε is added to both the numerator and denominator of the formula for calculating the detailed information of the FBP reconstructed image, and the parameter ε is used to avoid transmitting noise and the situation of being divided by zero;

[0101] In order to transmit the detailed information, first calculate the detailed layer of the FBP reconstructed image according to the following ratio, and calculate the detailed information F of the FBP reconstructed image DetailThe formula is as follows:

[0102]

[0103] In the formula, F represents the FBP reconstructed image, and F GIF is the guided image filtering result of F. This ratio captures the local detail changes in computer vision and is commonly referred to as the quotient image or ratio map. See Figure 2 , the advantage of using GIF instead of the classical low-pass Gaussian filter is that it can reduce halos.

[0104] Although the FBP reconstructed image contains detail information, it also contains noise, which may lead to the transmission of false details. Therefore, ε is added to the numerator and denominator of the formula for calculating the detail information F of the FBP reconstructed image to avoid transmitting noise and also avoid division by zero. Let ε = 9×10 Detail and ε = 9×10 -5 and ε = 9×10 -7 are respectively used for simulation experiments and real data experiments. To transmit the detail information, the final guided image D is calculated as follows: D = (1 - Μ)·F GIF ·F Detail + M·f (K+1)GIF .

[0105] See Figure 3 , in this embodiment, the FBP and SART reconstruction results of the projection data are denoted as F and S, and then the guided image filtering is performed respectively to obtain the corresponding results F GIF and S GIF . To better retain and transmit the detail information and improve the fineness and accuracy of the reconstructed image, the detail information F is calculated from F through . To provide a better initial value for the subsequent SART reconstruction, this detail layer is transmitted to F Detail . And it is combined with S GIF to obtain the final image D, as shown in D = (1 - Μ)·F GIF ·F GIF ·F Detail + M·f (K+1)GIF . And in the process of obtaining the initial value, the Μ calculated by is used as the weight to control the contributions of the information F GIF and S GIF extracted from two different sources in the initial value. Then D is used as the guided image to filter S GIF to obtain the image L GIF (S GIF ):

[0106]

[0107] In the formula, f (K+1)GIF is SGIF And L GIF (f (K+1)GIF ) represents the result of guiding image filtering for image f (K+1)GIF . i is the pixel index, and (a n , b n ) are the linear coefficients assumed to be constant in ω n . L i GIF (f (K+1)GIF ) is used as the initial value of the SART iteration, participates in the subsequent SART reconstruction process for iteration until the final image is obtained.

[0108] In this embodiment, the formula for using the initial value of the SART iteration to participate in the SART reconstruction process for iteration is:

[0109]

[0110] The relaxation coefficient λ K satisfies:

[0111]

[0112] In the formula, is the formula after iteration, is the formula before iteration; K = 0, 1…, λ K > 0, is the relaxation coefficient; a ij is the contribution of the jth pixel to the ith X-ray; p i is the projection data collected by the detector; is the linear attenuation coefficient of the nth pixel of the object to be measured at the Kth iteration; M, N are the orders of the positive definite diagonal matrices.

[0113] To more clearly explain the method proposed in this embodiment, the corresponding pseudo-code is given as shown in Algorithm 1.

[0114]

[0115] In this embodiment, simulation experiments and real experiments are used to verify and evaluate the proposed method, named SART-DT. Six comparison algorithms are selected, including the SART method, the FBP method, SART-TV, SART-L 0, SART-GIF, and FBP-GIF. Among them, the FBP-GIF method refers to performing guided image filtering on the result of each iteration of SART, with the FBP reconstruction result as the guiding image. The SART-GIF method performs guided image filtering on the result of each iteration of SART, and the guiding image is itself. The sparse angle reconstructions in the experiment were all carried out under the condition of sampling once every four angles within the range of 0 to π. To quantitatively evaluate the reconstruction effects of each comparative algorithm, structural similarity (SSIM), peak signal-to-noise ratio (PSNR), and mean square error (MSE) were used as evaluation indicators in this work.

[0116] In the simulation experiment, the SART-DT method was used to reconstruct the projection data of pigeons. To more clearly display the details of the image, two regions of interest were selected in the image results, marked with red and green rectangles and magnified, as Figure 4 shown. From these locally magnified regions, the image reconstruction effect of the SART-DT algorithm can be more clearly observed and compared with other comparative algorithms.

[0117] From Figure 4 (c), it can be seen that obvious strip artifacts still exist in the result reconstructed by FBP, while the strip artifacts in the image reconstructed by FBP-GIF have been reduced. As shown in Figure 4 (b), by observing the locally magnified region of the SART-reconstructed image, it can be seen that there are fewer artifacts, but the detailed structure is not clear enough. The results of the SART-TV method can be seen in both Figure 4 the two locally magnified regions of (d), and some detailed information is lost. The results of the SART-L 0 method are as shown in Figure 4 (e). In the green magnified region, the background texture is smoothed, while in the red magnified region, the image edges are not very clear. Figure 4-3 (f) and (h), from a subjective perspective, the reconstructed images of the SART-GIF method and the SART-DT method have similar reconstruction effects, the stripe artifacts are significantly suppressed, the detailed texture is improved, and it is also relatively clear.

[0118] Table 1 gives the comparison of the reconstruction performances of various methods. It can be clearly seen from Table 1 that the SSIM and PSNR values of the image reconstructed by the SART-DT method are the largest, and the MSE value is the smallest. That is to say, among the comparative algorithms, the SART-DT algorithm has the best reconstructed image effect.

[0119] Table 1 Evaluation index values of the results of different reconstruction methods in the simulation experiment.

[0120]

[0121] To more intuitively evaluate the reconstruction performance of different methods, Figure 5 shows the relative error results of each method compared with the ground truth as the number of iterations increases. It can be seen that among all the comparison methods, the SART method has the largest relative error value at the beginning of the iteration and decreases significantly as the number of iterations increases, but finally converges to about 0.13. The relative errors of SART-GIF and FBP-GIF almost all decrease from 0.56 to about 0.12. The relative error results of SART-L 0 are as shown in Figure 5 (b). When λ is 0.0001, SART- converges to a relatively high relative error, and when λ takes other values, it also converges to about 0.12. Figure 5 (c) in shows the comparison of the relative error convergence curves of the SART-TV algorithm and the SART-DT method under different smoothing parameter λ values. It can be seen from the convergence curves that SART-TV basically converges from 0.56 to 0.12. The relative error value of the SART-DT method is smaller at the beginning of the iteration, decreases as the number of iterations increases, and finally converges to about 0.09, which is lower than the convergence results of other methods.

[0122] In the real experiment, the SART-DT method was used to reconstruct the real projection data, and the comparative algorithms were applied to reconstruct the images, and finally the experimental results were compared. To more clearly see the key features, regions with complex detailed structures were selected to magnify them, and these regions are marked with red boxes in Figure 6 and are located in the upper left corner of each image.

[0123] Figure 6 Since the regions selected by the red boxes in the images in have very rich detailed structures and contain many high-frequency components, so from Figure 6 (b) and (c), the reconstruction by SART is not as clear as that of FBP, but the reconstruction result of FBP is streaky and has more artifacts. In Figure 6 (d), the details and background artifacts are smoothed to a certain extent, resulting in less clear image structures. In Figure 6 (e), after being processed by the SART- method, many details of the overall image are erased and a serious loss of information occurs. In Figure 6 (f), the reconstruction result of FBP-GIF contains slight stripe artifacts. Compared with FBP-GIF, the reconstruction result using SART-GIF has fewer artifacts and slightly worse texture structures, as shown in Figure 6 (g). In Figure 6 (h), the reconstruction result of SART-DT can effectively remove stripe artifacts while maintaining complex detailed structures.

[0124] Table 2 presents the numerical evaluation metrics (SSIM, PSNR, MSE) of the reconstruction results of each algorithm. It can be seen that FBP has the best SSIM value, while SART-DT has the highest PSNR value and the smallest MSE value. The reason may be that the real projection data contains more high-frequency information. FBP has a better ability to recover high-frequency information, so it has a higher structural similarity. However, it will produce a large number of stripe artifacts, while SART-DT can effectively remove stripe artifacts and contains rich detail information under the action of detail transfer. Generally speaking, the values of PSNR and MSE are the best.

[0125] Evaluation metric values of the results of different reconstruction methods in the real experiment.

[0126]

[0127] The relative errors calculated from the 15-iteration results of each reconstruction method and the images reconstructed from the complete projection data are as Figure 7 shown by the curves. It can be seen from Figure 7 that the relative errors of the SART algorithm and the SART-GIF algorithm fluctuate greatly in the early stage of iteration and finally tend to 0.107 and 0.1 respectively. In the initial stage of iteration, the relative error of the FBP-GIF method is close to and slightly higher than that of the SART-DT method, and finally converges to about 0.057. The relative error of the SART-L 0 method converges to about 0.12 under different smoothing parameter values, corresponding to different degrees of downward trends. The relative error of the SART-TV method in the first iteration is close to that of the SART-DT method, but the convergence amplitude is not as good as that of the SART-DT method, and the final convergence value is higher than that of the SART-DT method. The relative error of the SART-DT method converges between 0.09 - 0.03, which is the smallest among all algorithms. It can be seen that the reconstruction effect of SART-DT is the best.

[0128] See Figure 8 , in order to evaluate the reconstruction performance of SART-DT from multiple aspects, a fixed position is selected in each reconstructed image, and a line segment divided into two colors is drawn. The red part is located in the area with complex structure, and the yellow part is located in the simple background area. Observe the pixel values of the images obtained by each reconstruction method at the same position and compare them with the pixel values of the original image. For example, the position of the line segment in the SART-DT reconstructed image is as Figure 8 shown in (a). Compare the pixel values obtained from the straight lines on all reconstructed images, as shown in the remaining figures in Figure 8 . It can be found from the comparison of the gray curves that the gray curve of the SART-DT method is the closest to the gray curve of the original model, indicating that the method of the present invention has a better ability to restore image details and remove stripe artifacts.

[0129] Example 2

[0130] See Figure 9 , Example 2 of the present invention also provides a CT image reconstruction system based on ridge regression and detail conduction, including:

[0131] A projection data reconstruction module 001, configured to perform FBP reconstruction and SART reconstruction on projection data respectively to obtain an FBP reconstructed image and an SART reconstructed image;

[0132] A guided image filtering module 002, configured to perform guided image filtering based on ridge regression on the FBP reconstructed image and the SART reconstructed image respectively to obtain an FBP reconstructed image filtering result and an SART reconstructed image filtering result;

[0133] A guided image reconstruction module 003, configured to construct a mask, and fuse the FBP reconstructed image filtering result and the SART reconstructed image filtering result through the mask to obtain a guided image;

[0134] A detail layer analysis module 004, configured to calculate the detail information of the FBP reconstructed image, capture the local detail changes of the FBP reconstructed image, and obtain the detail layer result of the FBP reconstructed image;

[0135] A final image generation module 005, configured to combine the calculated detail layer result of the FBP reconstructed image with the FBP reconstructed image filtering result, and fuse the mask with the SART reconstructed image filtering result to obtain a final image;

[0136] An initial value generation module 006, configured to filter the SART reconstructed image filtering result with the final image as a guided image to obtain an initial value for SART iteration;

[0137] An iterative reconstruction module 007, configured to participate the initial value of the SART iteration in the SART reconstruction process for iteration until a final reconstructed image is obtained.

[0138] In this embodiment, in the guided image filtering module 002, the filtering output object is a linear transformation of the guided image in a square window centered on a pixel, and the linear coefficient is determined by minimizing a cost function including a regularization parameter.

[0139] In this embodiment, in the guided image reconstruction module 003:

[0140] Calculate the difference between the linearized data of the FBP reconstructed image filtering result and the SART reconstructed image filtering result, compare the difference of the linearized data with a set threshold, and determine the mask value according to the comparison result.

[0141] In this embodiment, in the detail layer analysis module 004, a parameter ε is added to both the numerator and denominator of the formula for calculating the detail information of the FBP reconstructed image, and the parameter ε is used to avoid the transmission of noise and the situation of division by zero.

[0142] Calculate the detail information F of the FBP reconstructed image Detail The formula is:

[0143]

[0144] In the formula, F represents the FBP reconstructed image, and F GIF is the guided image filtering result of F.

[0145] In this embodiment, in the iterative reconstruction module 007, the formula for iteratively participating the initial value of the SART iteration in the SART reconstruction process is:

[0146]

[0147] The relaxation coefficient λ K satisfies:

[0148] 0 ≤ ε ≤ λ K ≤ (2 - ε) / max{W i ∣ i = 1, 2, …, M}

[0149]

[0150] In the formula, is the formula after iteration, is the formula before iteration; K = 0, 1 …, λ K > 0, is the relaxation coefficient; a ij is the contribution of the j-th pixel to the i-th X-ray; p i is the projection data collected by the detector; f n (K) is the linear attenuation coefficient of the n-th pixel of the object to be measured at the K-th iteration; M, N are the orders of the positive definite diagonal matrices.

[0151] It should be noted that the information interaction, execution process, etc. between the above-mentioned system modules, because they are based on the same concept as the method embodiment in Embodiment 1 of this application, the technical effects brought by them are the same as those of the method embodiment of this application. For the specific content, reference can be made to the description in the method embodiment shown above in this application, and details will not be repeated here.

[0152] Embodiment 3

[0153] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which program code for a CT image reconstruction method based on ridge regression and detail conduction is stored, and the program code includes instructions for executing the CT image reconstruction method based on ridge regression and detail conduction according to Embodiment 1 or any possible implementation thereof.

[0154] The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that integrates one or more available media. The available medium can be a magnetic medium (for example, a floppy disk, a hard disk, a magnetic tape), an optical medium (for example, a DVD), or a semiconductor medium (for example, a solid-state drive (SSD)).

[0155] Embodiment 4

[0156] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0157] The processor and the memory communicate with each other through a bus; the memory stores program instructions executable by the processor, and the processor can execute the CT image reconstruction method based on ridge regression and detail conduction according to Embodiment 1 or any possible implementation thereof by invoking the program instructions.

[0158] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor, which is implemented by reading software code stored in the memory. The memory can be integrated in the processor or can be located outside the processor and exist independently.

[0159] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions according to the embodiments of the present invention are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.).

[0160] Obviously, those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computing device. They can be concentrated on a single computing device or distributed on a network composed of multiple computing devices. Optionally, they can be implemented by program codes executable by the computing device. Thus, they can be stored in a storage device and executed by the computing device. And in some cases, the steps shown or described can be executed in a sequence different from that here, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. In this way, the present invention is not limited to any specific combination of hardware and software.

[0161] Although the present invention has been described in detail above with general descriptions and specific embodiments, on the basis of the present invention, some modifications or improvements can be made, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of the present invention claimed.

Claims

1. A CT image reconstruction method based on ridge regression and detail conduction, characterized in that: include: Perform FBP reconstruction and SART reconstruction on the projection data to obtain FBP reconstructed images and SART reconstructed images, perform guided image filtering based on ridge regression on the FBP reconstructed images and the SART reconstructed images to obtain FBP reconstructed image filtering results and SART reconstructed image filtering results; Constructing a mask, through which the filtering result of the FBP reconstructed image is fused with the filtering result of the SART reconstructed image to obtain a guide image; Calculate the detail information of the FBP reconstructed image, capture the local detail changes of the FBP reconstructed image, and obtain the detail layer result of the FBP reconstructed image; The calculated detail layer result of the FBP reconstructed image is combined with the filtering result of the FBP reconstructed image, and the mask is fused with the filtering result of the SART reconstructed image to obtain a final image, and the filtering result of the SART reconstructed image is filtered using the final image as a guide image to obtain an initial value of the SART iteration; The initial value of the SART iteration is involved in the SART reconstruction process for iteration until a final reconstructed image is obtained.

2. The CT image reconstruction method based on ridge regression and detail conduction according to claim 1, characterized in that: In the guided image filtering based on ridge regression, the filtering output object is a linear transformation of the guided image in a square window centered on a pixel, and the linear coefficient is determined by minimizing a cost function including a regularization parameter.

3. The CT image reconstruction method based on ridge regression and detail conduction according to claim 1, characterized in that: During the mask construction process: The difference between the linearized data of the FBP reconstructed image filtering result and the SART reconstructed image filtering result is calculated, the difference between the linearized data is compared with the set threshold, and the mask value is determined according to the comparison result.

4. The CT image reconstruction method based on ridge regression and detail conduction according to claim 1, characterized in that: In the process of calculating the detail information of the FBP reconstructed image, the parameter ε is added to the numerator and denominator of the formula for calculating the detail information of the FBP reconstructed image, and the parameter ε is used to avoid the transmission of noise and the occurrence of division by zero; Calculate the detail information F of the FBP reconstructed image Detail The formula is: Where, F represents the FBP reconstructed image, F GIF is the guided image filtering result of F.

5. The CT image reconstruction method based on ridge regression and detail conduction according to claim 4, characterized in that: The formula for iterating the initial value of the SART iteration in the SART reconstruction process is: Relaxation coefficient λ K satisfy: 0≤e≤l K ≤(2-ε) / max{W i ∣i=1,2,…,M} In the formula, is the formula after iteration, is the formula before iteration; K=0,1…,λ K >0, is the relaxation coefficient; a ij is the contribution of the j-th pixel to the i-th X-ray; p i projection data collected for the detector; is the linear attenuation coefficient of the nth pixel of the measured object at the Kth iteration; M and N are the orders of the positive definite diagonal matrix.

6. A CT image reconstruction system based on ridge regression and detail conduction, characterized in that: include: A projection data reconstruction module is used to perform FBP reconstruction and SART reconstruction on the projection data to obtain an FBP reconstructed image and a SART reconstructed image; A guided image filtering module is used to perform guided image filtering based on ridge regression on the FBP reconstructed image and the SART reconstructed image, respectively, to obtain the FBP reconstructed image filtering result and the SART reconstructed image filtering result; A guided image reconstruction module is used to construct a mask, through which the FBP reconstructed image filtering result and the SART reconstructed image filtering result are fused to obtain a guided image; The detail layer analysis module is used to calculate the detail information of the FBP reconstructed image, capture the local detail changes of the FBP reconstructed image, and obtain the detail layer results of the FBP reconstructed image; A final image generation module is used to combine the calculated detail layer result of the FBP reconstructed image with the FBP reconstructed image filtering result, and fuse the mask with the SART reconstructed image filtering result to obtain a final image; An initial value generation module is used to filter the SART reconstruction image filtering result using the final image as a guide image to obtain an initial value of the SART iteration; The iterative reconstruction module is used to involve the initial value of the SART iteration in the SART reconstruction process for iteration until a final reconstructed image is obtained.

7. The CT image reconstruction system based on ridge regression and detail conduction according to claim 6, characterized in that: In the guided image filtering module, the filtering output object is a linear transformation of the guided image in a square window centered on a pixel, and the linear coefficient is determined by minimizing a cost function including a regularization parameter.

8. The CT image reconstruction system based on ridge regression and detail conduction according to claim 6, characterized in that: In the guided image reconstruction module: The difference between the linearized data of the FBP reconstructed image filtering result and the SART reconstructed image filtering result is calculated, the difference between the linearized data is compared with the set threshold, and the mask value is determined according to the comparison result.

9. The CT image reconstruction system based on ridge regression and detail conduction according to claim 6, characterized in that: In the detail layer analysis module, the parameter ε is added to the numerator and denominator of the formula for calculating the detail information of the FBP reconstructed image, and the parameter ε is used to avoid the transmission of noise and the occurrence of division by zero; Calculate the detail information F of the FBP reconstructed image Detail The formula is: Where, F represents the FBP reconstructed image, F GIF is the guided image filtering result of F.

10. The CT image reconstruction system based on ridge regression and detail conduction according to claim 9, characterized in that: In the iterative reconstruction module, the formula for iterating the initial value of the SART iteration in the SART reconstruction process is: Relaxation coefficient λ K satisfy: 0≤e≤l K ≤(2-ε) / max{W i ∣i=1,2,…,M} In the formula, is the formula after iteration, is the formula before iteration; K=0,1…,λ K >0, is the relaxation coefficient; a ij is the contribution of the j-th pixel to the i-th X-ray; p i projection data collected for the detector; f n (K) is the linear attenuation coefficient of the nth pixel of the measured object at the Kth iteration; M and N are the orders of the positive definite diagonal matrix.

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