An electronic tomographic image denoising method based on block matching four-dimensional collaborative filtering

Abstract

The application discloses a kind of based on block matching four-dimensional collaborative filtering electronic tomography image denoising method, the method is to utilize the rich structural information of electronic tomography image, traditional block matching denoising method can blur edge, excessive smoothness loses structural information, edge structure has important role for subsequent three-dimensional macromolecular identification, classification and average.Because of the existence of noise and the limited search range of similar block, the matching accuracy of similar block is not high, and the non-similar points in the image block will cause edge blur in the result of BM4D algorithm after filtering and weighted averaging. To solve this problem, the application proposes an edge image block classification-based similarity measurement method to improve the matching degree of similar blocks, which preserves the edge structural information while denoising.

Description

Technical Field

[0001] This invention belongs to the fields of cryo-electron tomography image processing and computer vision technology, and particularly relates to an electron tomography image denoising method based on block matching four-dimensional collaborative filtering. Background Technology

[0002] Cryo-electron tomography (cryo-electron computed tomography) has become an important tool for reconstructing the three-dimensional structures of biomolecules at nanoscale resolution through electron microscopic projection images, attracting increasing attention. However, due to the low electron dose and limited sampling angle, electron tomography images typically have a low signal-to-noise ratio, affecting subsequent image analysis and understanding, thus burying useful structural information in noise.

[0003] Designing a reasonable denoising method for 3D electron tomography images remains a major challenge. The Block-matching and 4D filtering algorithm (BM4D) fully utilizes the sparsity and local similarity of images, achieving excellent denoising results for 3D data and has been widely applied in various medical image denoising applications. However, this algorithm has certain limitations. Good denoising results can only be achieved when a sufficient number of high-quality similar blocks are matched to the reference 3D image block. If the similarity block matching degree is low, problems such as edge blurring and "block artifacts" will occur, leading to a sharp decline in denoising performance.

[0004] Therefore, there is an urgent need for a technical solution that can protect the edge information of electron tomography images while achieving noise reduction. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a block-matching four-dimensional collaborative filtering method for electron tomography image denoising, which addresses the problem that electron tomography image denoising methods struggle to preserve edge structures and texture details when removing noise.

[0006] A method for denoising electron tomography images based on block-matching four-dimensional collaborative filtering, comprising the following steps:

[0007] (1) Matching similar blocks in noisy images: First, similar blocks are grouped using the idea of ​​nonlocality. In the noisy image, n similar blocks are found with a specified window size as the reference image block, forming a four-dimensional matrix. The similar structure is transformed by image block matching, that is, matching is performed by utilizing the sparsity and structural similarity of image blocks; the value of n is 2. m m≥2;

[0008] (2) Collaborative hard thresholding filtering: The four-dimensional matrix formed by the set of similar blocks is processed by four-dimensional transformation. The four-dimensional transformation utilizes the correlation between similar blocks to express the real signal in the set of similar blocks in a sparse form. Noise is filtered out by the hard thresholding shrinkage coefficient method. Then, the basic estimation results of all image blocks are obtained by performing a four-dimensional inverse transformation on the filtered coefficients, thus completing the collaborative filtering.

[0009] (3) Image patch aggregation weighted average: When the same image patch is located in different sets of similar patches, the basic estimate of the image patch after the four-dimensional inverse transformation has multiple estimates. Then, the image patch estimation results need to be weighted and averaged to obtain the estimate of each voxel point, i.e. the basic estimation result.

[0010] (4) Three-dimensional edge image block detection: Since electron tomography images contain a lot of important edge structure information, the edge points of electron tomography images are extracted using three-dimensional gradient information. The image block is judged to be an edge image block based on the proportion of edge points in the image block. The edge structure of the edge image block containing edge structure information is the area where the local intensity of the image gray value changes significantly, and it is the boundary line of the main area.

[0011] Specifically, the different similarity measurement methods are as follows: the non-edge image patches are measured using Euclidean distance, while the edge image patches are measured using gradient magnitude similarity. When a reference image patch has an edge structure, it is considered an edge image patch. Image patches with structures more similar to the reference image patch are selected, and collaborative filtering between candidate image patches and reference image patches is used to protect structural information from being blurred. That is, the gradient magnitude similarity (GMS) of the reference image patch and candidate image patches is calculated, and the gradient magnitude standard deviation (GMSD) between image patches is statistically analyzed to determine the degree of similarity.

[0012] (5) Basic estimation similar block matching: The similar block grouping is performed on the basic estimation result obtained in step (3). In the basic estimation result, n similar blocks are found with a specified window size as the reference image block to form a four-dimensional matrix. Different similarity measurement methods are used according to whether they are edge image blocks. After finding the similar block set position of the reference image block in the basic estimation result, the image blocks at the same position are extracted on the noisy image to obtain two four-dimensional matrices respectively. The two four-dimensional matrices are respectively from the noisy image and the basic estimation image. The value of n is 32.

[0013] (6) Collaborative Wiener filtering: Perform a four-dimensional transformation on the two four-dimensional matrices obtained by grouping similar blocks, use the energy spectrum of the basic estimated four-dimensional matrix as the guide for empirical Wiener filtering of the four-dimensional matrix of the noisy image, and the overlapping image blocks obtained after filtering have multiple estimated voxels. Inverse transform the four-dimensional matrix of the noisy image back to the corresponding position of the image block.

[0014] (7) Image patch aggregation weighted average: The voxels of the multiple estimated values ​​obtained after filtering in step (6) are weighted to obtain the final estimation result, i.e. the final denoising result.

[0015] Furthermore, in step (1), n ​​similar blocks are found using a specified window size as a reference image block. When n is 16, the speed and effect of finding similar blocks are optimal.

[0016] Further, in step (1), the similarity of image blocks is calculated using Euclidean distance to perform noisy image similarity block matching, forming a four-dimensional matrix. Specifically, image block P represents the reference block, and image blocks similar to it are searched within a local range of the image space. The similarity of image blocks is calculated using Euclidean distance. The Euclidean distance between the reference image block P and the candidate image block Q of size L×L×L is calculated as follows:

[0017]

[0018] in Indicate l 2 The smaller the norm and Euclidean distance d(P,Q), the more similar the two image patches are. If the distance between a candidate patch and a reference patch is less than a given threshold, the candidate patch is added to the set S of similar patches of the current reference patch. p The definition is as follows:

[0019] S P ={P∈X: d(P, Q)<τ hard}

[0020] Where x represents the image domain, τ hard This represents the maximum distance threshold for grouping in the basic estimation stage; the set of similar blocks S is obtained. P Then, it is combined with the current reference block to form a four-dimensional matrix block.

[0021] Furthermore, in step (2), a four-dimensional transformation is performed on the four-dimensional matrix formed by the set of similar blocks, and noise is filtered out by the hard threshold shrinkage coefficient method. The mathematical expression of the hard threshold collaborative filtering is as follows:

[0022]

[0023] Where P(P) represents a set of similar image patches S P The three-dimensional matrix formed This represents the four-dimensional transformation of the hard thresholding stage, where γ represents the given threshold parameter. Perform hard threshold filtering.

[0024] Further, in step (4), edge points of the 3D image are extracted using an edge detection operator. The proportion of edge points determines whether an image is an edge patch. Edge points are detected by setting a gradient magnitude threshold, thus obtaining the edge... Figure 2 Value map, calculate the edge voxel ratio of the entire 3D image:

[0025]

[0026] Where, N e The number of edge voxels in the edge map is represented by N1×N2×N3, which calculates the total number of voxels in the 3D image. When determining whether an image patch is an edge patch, the edge voxel ratio of the image patch is calculated as follows:

[0027]

[0028] Where, N b Represents the number of edge points of an image patch, if R b If the value is greater than R, the image patch is considered an edge image patch; otherwise, it is a non-edge image patch. Edge image patches contain edge structure information. Different similarity measurement methods are used to distinguish between edge image patches and non-edge image patches before collaborative filtering is performed to preserve the edge structure.

[0029] Furthermore, the formula for calculating the gradient magnitude similarity (GMS) of the reference image patch and the candidate image patch in step (4) is as follows:

[0030]

[0031] Where P represents the reference image patch, Q represents the candidate image patch, mag(i) represents the gradient magnitude at voxel point i, c is a fixed positive integer used to provide numerical stability, and GMS reflects the degree of local structural similarity between two image patches. If the gradient magnitudes of P and Q at spatial position i are the same, GMS(i) can reach a maximum value of 1. The gradient magnitude similarity mean (GMSM) is calculated as follows:

[0032]

[0033] Where L 3 This represents the number of voxels in an image patch. Since the magnitude of the GMSM value is positively correlated with the similarity of the gradient structures of two image patches, the overall similarity of image patches is measured by combining GMS and GMSM. The gradient magnitude standard deviation (GMSD) is then calculated.

[0034]

[0035] The smaller the GMSD, the higher the structural similarity of the image blocks. GMSD can be used to measure the local structural similarity of image blocks, and can find more structurally similar image blocks in the block matching stage, thus matching the more structurally similar image blocks.

[0036] Furthermore, in step (5), different similarity measurement methods are used depending on whether it is an edge image block. Specifically, the gradient magnitude similarity measurement method is used for edge image blocks, and the Euclidean distance similarity measurement method is used for non-edge image blocks.

[0037] Furthermore, the Wiener filter in step (6) is represented by the following formula:

[0038]

[0039] Where σ 2 P represents the noise variance. basic (P) represents the basic estimated block matching result. This represents the four-dimensional transformation of the collaborative Wiener filtering stage;

[0040] Therefore, the process of performing Wiener filtering and then inverse transform on a four-dimensional matrix can be represented as follows:

[0041]

[0042] Where P wien (P) represents the set of image patches after collaborative Wiener filtering. This represents the four-dimensional inverse transformation.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] This invention addresses the denoising of cryo-electron tomography (CETT) images. A four-dimensional collaborative filtering denoising method based on gradient information and block matching improves the quality of three-dimensional CETT images. Since CETT images possess rich structural information, edge image block classification and gradient magnitude-based similarity metrics enhance the matching degree of similar blocks, preserving edge structural information while denoising. This invention improves image quality while retaining edge structure and texture details, which is beneficial for subsequent analysis and interpretation of CETT images. Attached Figure Description

[0045] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0046] Figure 1 This is a schematic diagram of 3D image patch matching;

[0047] Figure 2XYZ cross-sectional views of the original electron tomography image and gradient amplitude map;

[0048] Figure 3 A similarity measurement method for reference blocks and candidate image blocks;

[0049] Figure 4 Here are Z-direction cross-sectional views of the noisy electron tomography image and the denoised image;

[0050] Figure 5 for Figure 4 The blue box highlights a magnified view of the details. Detailed Implementation

[0051] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0052] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0053] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described below in conjunction with the embodiments and accompanying drawings.

[0054] A method for denoising electron tomography images based on block-matching four-dimensional collaborative filtering, comprising the following steps:

[0055] (1) First stage: Noisy image similarity block matching. Similar blocks are found in the noisy image using a specified window size as a reference block, forming a four-dimensional matrix. The search process for similar blocks in the three-dimensional image is as follows: Figure 1 As shown. Image patch P represents a reference patch, and image patches similar to it are searched within a local area of ​​the image space. Euclidean distance is used to calculate the similarity of image patches. The Euclidean distance calculation method for a reference image patch P and a candidate image patch Q of size L×L×L is as follows:

[0056]

[0057] in Indicate l 2The smaller the norm and Euclidean distance d(P,Q), the more similar the two image patches are. If the distance between a candidate patch and a reference patch is less than a given threshold, the candidate patch is added to the set S of similar patches of the current reference patch. p The definition is as follows:

[0058] S P ={P∈X: d(P, Q)<τ hard}

[0059] Where X represents the image domain, τ hard This represents the maximum distance threshold for grouping during the basic estimation stage. The set of similar blocks S is obtained. P Then, it is combined with the current reference block to form a four-dimensional matrix block.

[0060] (2) Collaborative Hard Thresholding Filtering. A four-dimensional transformation is performed on the four-dimensional matrix formed by the set of similar blocks. This transformation utilizes the correlation between similar blocks to express the true signal in the set of similar blocks in a sparse form. Noise is filtered out using a hard thresholding method to shrink the coefficients. Then, a four-dimensional inverse transformation is performed on the filtered coefficients to obtain the basic estimation results for all image blocks, thus achieving collaborative filtering. The advantage of collaborative filtering is that it improves the estimation result of each image block after filtering, and errors caused by mismatches in a single image block have a smaller impact on the estimation results of other image blocks. Hard thresholding collaborative filtering is represented as follows:

[0061]

[0062] Where P(P) represents a set of similar image patches S P The three-dimensional matrix formed This represents the four-dimensional transformation of the hard thresholding stage, where γ represents the given threshold parameter. Perform hard threshold filtering.

[0063] (3) Image patch aggregation and weighted averaging. Since the same image patch may be located in different sets of similar patches, the basic estimate of the image patch after the four-dimensional inverse transform may have multiple estimates. Therefore, it is necessary to perform a weighted average of the image patch estimation results to obtain the final estimate of the voxel points. For example, if the similar image patches of reference image patch P1 include reference image patch P2 and reference image patch P3, the basic estimates of P1, P2, and P3 are obtained after collaborative filtering. When P2 is used as the reference patch, the similar patches including P1 and P3 will also yield the estimates of P1, P2, and P3. Therefore, it is necessary to perform a weighted average of the image patch estimation results to obtain the final estimate of the voxel points.

[0064] (4) 3D edge image patch detection. Edge points in the 3D image are located using an edge detection operator based on gradient information. Edge image patches are distinguished from non-edge image patches based on the proportion of edge points contained within them. Edge image patches contain rich edge structure information. Different similarity measurement methods are used to distinguish edge image patches from non-edge image patches, and then collaborative filtering is performed to preserve important edges. The original electron tomography image and the corresponding gradient magnitude map are shown below. Figure 2 As shown.

[0065] (5) Second-stage similarity block grouping. Unlike step (1), the second-stage similarity block grouping is performed based on the results of the baseline estimation. Different similarity measures are used depending on whether the image block is an edge image block. Euclidean distance is used to measure the similarity of non-edge image blocks, while gradient magnitude similarity is used to measure the similarity of edge image blocks. Figure 3 As shown, reference image block P exhibits a clear edge structure and is classified as an edge image block. If Euclidean distance is used to measure similarity, candidate image block Q1 in the lower left corner is more similar to reference image block P. However, from a visual perspective, candidate image block Q2 in the lower right corner is structurally more similar to reference image block P. Collaborative filtering between the lower right image block and the reference block can better protect structural information from obscuring it. The gradient magnitude similarity (GMS) calculation formula between reference image block P and candidate image block Q is as follows:

[0066]

[0067] Where mag(i) represents the gradient magnitude at voxel point i in space, c is a fixed positive integer used to provide numerical stability, and GMS reflects the degree of local structural similarity between two image patches. If the gradient magnitudes of images P and Q at spatial location i are the same, GMS(i) can reach a maximum value of 1. The gradient magnitude similarity mean (GMSM) is calculated as follows:

[0068]

[0069] Where L 3 This represents the number of voxels in an image patch. Clearly, a larger GMSM value indicates a higher degree of similarity in the gradient structures of two image patches. Combining GMS and GMSM measures the overall similarity of image patches, we calculate the gradient magnitude similarity deviation (GMSD).

[0070]

[0071] The smaller the GMSD, the higher the structural similarity of the image blocks. GMSD can be used to measure the local structural similarity of image blocks, and can find more structurally similar image blocks in the block matching stage, thus matching the more structurally similar image blocks.

[0072] After finding the location of the set of similar blocks to the reference block of the base estimate, image blocks at the same locations are extracted from the noisy image, resulting in two four-dimensional matrices. One four-dimensional matrix comes from the noisy image, and the other comes from the base estimate image.

[0073] Step (6), Cooperative Wiener Filtering. Perform a four-dimensional transformation on the two four-dimensional matrices obtained by grouping similar blocks. Use the fundamentally estimated four-dimensional matrix as the energy spectrum of the true signal to guide the empirical Wiener filtering of the four-dimensional matrix of the noisy image. Perform an inverse transformation on the four-dimensional matrix of the noisy image back to the corresponding position of the image block. The Wiener filter is expressed by the following formula:

[0074]

[0075] Where σ 2 P represents the noise variance. basic (P) represents the basic estimated block matching result. This represents the four-dimensional transformation of the collaborative Wiener filtering stage.

[0076] Therefore, the process of performing Wiener filtering and inverse transform on a four-dimensional matrix can be represented as follows:

[0077]

[0078] Where P wien (P) represents the set of image patches after collaborative Wiener filtering. This represents the four-dimensional inverse transformation.

[0079] Step (7): Image patch aggregation and weighted averaging. A weighted average is performed on voxels with multiple estimates to obtain the final estimation result. The Z-direction cross-section of the noisy electron tomography image and the denoised result image is shown below. Figure 4 As shown, Figure 4 The blue box highlights a magnified view of the details, as shown in the image. Figure 5 As shown.

[0080] Example

[0081] This set of experimental data uses data from -61... ° ~+65 ° Projection angle range, with a projection interval of 2. °A total of 64 projected images were obtained. After 3D reconstruction, a 3D electron tomography image with a size of 1024×1024×300 was obtained, and the images were normalized. The electron tomography image denoising method based on spatial similarity and block matching four-dimensional collaborative filtering, as described in this invention, was applied to this set of data, including the following steps:

[0082] S1, First stage similarity block matching. For a noisy 3D electron tomography image, a similar image block Q is searched within an image window centered on the current reference image block P. The size of the search 3D window is N×N×N, where N is 39, the sliding step size is p=3, and the similarity threshold τ=0.1.

[0083] In S1, finding similar image blocks Q involves searching for n similar blocks with a specified window size as the reference image block. That is, searching for similar image blocks within a local range of the image space. When n is 16, the speed and effect of finding similar blocks are optimal.

[0084] In S1, finding similar image blocks Q involves searching for n similar blocks with a specified window size as the reference image block. That is, searching for similar image blocks within a local range of the image space. When n is 16, the speed and effect of finding similar blocks are optimal.

[0085] S2, Collaborative Hard Thresholding Filtering. A four-dimensional transformation is performed on the four-dimensional matrix formed by the set of similar blocks. This transformation utilizes the correlation between similar blocks to express the true signal in the set in a sparse form. Noise is filtered out by shrinking the coefficients using hard thresholding. Then, a four-dimensional inverse transformation is performed on the filtered coefficients to obtain the basic estimation results for all image blocks, thus achieving collaborative filtering. The threshold for hard thresholding collaborative filtering is λ. 4D =2.7.

[0086] S3, Image Patch Aggregation Weighted Average. After collaborative filtering, the denoising result for each 3D image patch in the four-dimensional matrix is ​​obtained. These 3D image patches exhibit overlapping positions, meaning multiple estimates exist for each voxel value. To address this issue, image patch aggregation weighted average is used, i.e., the estimation results of the image patches are weighted to obtain the final estimation result. Weights It is expressed as follows:

[0087]

[0088] in This represents the number of non-zero coefficients after hard thresholding. It can be seen that image blocks with relatively high noise have smaller weights, effectively reducing noise. σ 2 This represents the noise variance.

[0089] S4, 3D edge image patch detection. Edge points in the 3D image are located using an edge detection operator based on gradient information. Considering the massive size of 3D electron tomography image data, using a 3D template for convolution would be too complex and require too much space. Therefore, the central difference formula is used to calculate the gradient of image grayscale along the x, y, and z directions. The calculation formula is as follows:

[0090] G x (i,j,k)=f(i+1,j,k)-f(i-1,j,k)

[0091] G y (i,j,k)=f(i,j+1,k)-f(i,j-1,k)

[0092] G z (i,j,k)=f(i,j,k+1)-f(i,j,k-1)

[0093] The gradient vector corresponding to position (i, j, k) is [G x G y G z ] T The corresponding gradient magnitude mag is calculated as follows:

[0094]

[0095] The magnitude of the gradient at a voxel reflects the degree of change at that point; a larger gradient magnitude indicates a sharper edge change.

[0096] Edge points are detected by setting a gradient magnitude threshold. A properly set threshold can filter out voxel points with high gradient magnitudes due to noise. Voxel points with low gradient magnitudes are removed by setting a gradient threshold, thus obtaining edge detection. Figure 2 Value map, calculate the edge voxel ratio of the entire 3D image:

[0097]

[0098] Where, N e The number of edge voxels in the edge map is represented by N1×N2×N3, which calculates the total number of voxels in the 3D image. When determining whether an image patch is an edge patch, the edge voxel ratio of the image patch is calculated as follows:

[0099]

[0100] Where N b Represents the number of edge points of an image patch, if R bIf the similarity is greater than R, the image patch is considered an edge patch; otherwise, it is a non-edge patch. Edge patches contain rich edge structure information. Different similarity metrics are used to distinguish between edge patches and non-edge patches, followed by collaborative filtering to preserve important edges.

[0101] S5, Second-stage similarity block grouping. The second-stage similarity block grouping is performed based on the results of the base estimation. Different similarity measures are used depending on whether the image patch is an edge patch. Euclidean distance is used to measure the similarity of non-edge image patches, while gradient magnitude similarity is used for edge image patches. After finding the location of the similarity block set of the reference block in the base estimation, image patches at the same location are extracted from the noisy image, resulting in two four-dimensional matrices. One four-dimensional matrix comes from the noisy image, and the other comes from the base estimation image.

[0102] S6, Collaborative Wiener Filtering. A four-dimensional transformation is performed on the two four-dimensional matrices obtained by grouping similar blocks. The estimated four-dimensional matrix is ​​then used as the energy spectrum of the true signal to guide the empirical Wiener filtering of the four-dimensional matrix of the noisy image. The inverse transformation of the four-dimensional matrix of the noisy image is then performed to return to the corresponding position of the image block. The Wiener filter is expressed by the following formula:

[0103]

[0104] Therefore, the process of performing Wiener filtering and inverse transform on a four-dimensional matrix can be represented as follows:

[0105]

[0106] S7, Image Patch Aggregation Weighted Average. A final estimate is obtained by weighting voxels with multiple estimates based on noise levels and Wiener filter coefficients.

[0107] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A method for denoising electron tomography images based on block-matching four-dimensional collaborative filtering, characterized in that: step: (1) Matching similar blocks in noisy images: First, similar blocks are grouped using the idea of ​​nonlocality. In the noisy image, n similar blocks are found with a specified window size as the reference image block, forming a four-dimensional matrix. The similar structure is transformed by image block matching, that is, matching is performed by utilizing the sparsity and structural similarity of image blocks; the value of n is 2. m m≥2; (2) Collaborative hard thresholding filtering: The four-dimensional matrix formed by the set of similar blocks is processed by four-dimensional transformation. The four-dimensional transformation utilizes the correlation between similar blocks to express the real signal in the set of similar blocks in a sparse form. Noise is filtered out by the hard thresholding shrinkage coefficient method. Then, the basic estimation results of all image blocks are obtained by performing a four-dimensional inverse transformation on the filtered coefficients, thus completing the collaborative filtering. (3) Image patch aggregation weighted average: When the same image patch is located in different sets of similar patches, the basic estimate of the image patch after the four-dimensional inverse transformation has multiple estimates. Then, the image patch estimation results need to be weighted and averaged to obtain the estimate of each voxel point, i.e. the basic estimation result. (4) Three-dimensional edge image block detection: Since electron tomography images contain a lot of important edge structure information, the edge points of electron tomography images are extracted using three-dimensional gradient information. The image block is judged to be an edge image block based on the proportion of edge points in the image block. The edge structure of the edge image block containing edge structure information is the area where the local intensity of the image gray value changes significantly, and it is the boundary line of the main area. Specifically, the different similarity measurement methods are as follows: for non-edge image patches, Euclidean distance is used to measure the similarity, while for edge image patches, gradient magnitude similarity is used to measure the similarity. When a reference image patch has an edge structure, it is considered an edge image patch. Image patches with structures more similar to the reference image patch are selected, and collaborative filtering between candidate image patches and reference image patches is used to protect structural information from being blurred. That is, the gradient magnitude similarity (GMS) of the reference image patch and candidate image patches is calculated, and the gradient magnitude standard deviation (GMSD) between image patches is statistically analyzed to determine the degree of similarity. (5) Basic estimation similar block matching: The similar block grouping is performed on the basic estimation result obtained in step (3). In the basic estimation result, n similar blocks are found with a specified window size as the reference image block to form a four-dimensional matrix. Different similarity measurement methods are used depending on whether the image patch is an edge. After finding the location of the similar patch set of the reference image patch in the basic estimation result, image patches at the same location are extracted on the noisy image to obtain two four-dimensional matrices. The two four-dimensional matrices are respectively from the noisy image and the basic estimation image. The value of n is 32. (6) Collaborative Wiener filtering: Perform a four-dimensional transformation on the two four-dimensional matrices obtained by grouping similar blocks, use the energy spectrum of the basic estimated four-dimensional matrix as the guide for empirical Wiener filtering of the four-dimensional matrix of the noisy image, and the overlapping image blocks obtained after filtering have multiple estimated voxels. Inverse transform the four-dimensional matrix of the noisy image back to the corresponding position of the image block. (7) Image patch aggregation weighted average: The voxels of the multiple estimated values ​​obtained after filtering in step (6) are weighted to obtain the final estimation result, i.e. the final denoising result.

2. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, In step (1), n ​​similar blocks are found using a specified window size as a reference image block. When n is 16, the speed and effect of finding similar blocks are optimal.

3. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, In step (1), the similarity of image blocks is calculated using Euclidean distance to perform noisy image similarity block matching, forming a four-dimensional matrix. Specifically, image block P represents the reference block, and image blocks similar to it are searched within a local range of the image space. The similarity of image blocks is calculated using Euclidean distance. The Euclidean distance between the reference image block P and the candidate image block Q of size L×L×L is calculated as follows: in Indicate l 2 The smaller the norm and Euclidean distance d(P,Q), the more similar the two image patches are. If the distance between a candidate patch and a reference patch is less than a given threshold, the candidate patch is added to the set S of similar patches of the current reference patch. p The definition is as follows: S P ={P∈X:d(P,Q)<τ hard } Where X represents the image domain, τ hard This represents the maximum distance threshold for grouping in the basic estimation stage; the set of similar blocks S is obtained. P Then, it is combined with the current reference block to form a four-dimensional matrix block.

4. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, In step (2), a four-dimensional transformation is performed on the four-dimensional matrix formed by the set of similar blocks, and noise is filtered out by the hard threshold shrinkage coefficient method. The mathematical expression of the hard threshold collaborative filtering is as follows: Where P(P) represents a set of similar image patches S P The three-dimensional matrix formed This represents the four-dimensional transformation of the hard thresholding stage, where γ represents the given threshold parameter. Perform hard threshold filtering.

5. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, In step (4), edge points of the 3D image are extracted using an edge detection operator. The proportion of edge points determines whether an image is an edge block. Edge points are detected by setting a gradient magnitude threshold, resulting in a binary edge map. The edge voxel ratio of the entire 3D image is then calculated. Where, N e The number of edge voxels in the edge map is represented by N1×N2×N3, which calculates the total number of voxels in the 3D image. When determining whether an image patch is an edge patch, the edge voxel ratio of the image patch is calculated as follows: Where, N b Represents the number of edge points of an image patch, if R b >R considers an image patch to be an edge image patch, otherwise it is a non-edge image patch; edge image patches contain edge structure information. After different similarity measurement methods are used to distinguish edge image patches from non-edge image patches, collaborative filtering is then performed to preserve the edge structure.

6. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, The formula for calculating the gradient magnitude similarity (GMS) of the reference image patch and the candidate image patch in step (4) is as follows: Where P represents the reference image patch, Q represents the candidate image patch, mag(i) represents the gradient magnitude at voxel point i, c is a fixed positive integer used to provide numerical stability, and GMS reflects the degree of local structural similarity between two image patches. If the gradient magnitudes of P and Q at spatial position i are the same, GMS(i) can reach a maximum value of 1. The gradient magnitude similarity mean (GMSM) is calculated as follows: Where L 3 This represents the number of voxels in an image patch. Since the magnitude of the GMSM value is positively correlated with the similarity of the gradient structures of two image patches, the overall similarity of image patches is measured by combining GMS and GMSM. The gradient magnitude standard deviation (GMSD) is then calculated. The smaller the GMSD, the higher the structural similarity of the image blocks. GMSD can be used to measure the local structural similarity of image blocks, and can find more structurally similar image blocks in the block matching stage, thus matching the more structurally similar image blocks.

7. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, In step (5), different similarity measurement methods are used depending on whether it is an edge image block. Specifically, the gradient magnitude similarity measurement method is used for edge image blocks, and the Euclidean distance similarity measurement method is used for non-edge image blocks.

8. The electron tomography image denoising method based on block-matching four-dimensional collaborative filtering according to claim 1, characterized in that, The Wiener filter in step (6) is represented by the following formula: Where σ 2 P represents the noise variance. basic (P) represents the basic estimated block matching result. This represents the four-dimensional transformation of the collaborative Wiener filtering stage; Therefore, the process of performing Wiener filtering and then inverse transform on a four-dimensional matrix can be represented as follows: Where P wien (P) represents the set of image patches after collaborative Wiener filtering. This represents the four-dimensional inverse transformation.

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