An Adaptive Details-Preserving Noise Reduction Method Based on Truncated Singular Values ​​and Principal Component Analysis

Abstract

This invention discloses an adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis (PCA), comprising: estimating noise in a global subsurface defect image to obtain eigenvalues ​​of a global noise matrix; dividing the original noisy image into overlapping image blocks, and using an adaptive clustering method to obtain different block group matrices composed of similar image blocks, each block group matrix corresponding to a feature classification; performing adaptive truncated singular value denoising on each block group matrix to obtain a low-noise clustering matrix; processing the low-noise clustering matrix using adaptive PCA to obtain image blocks; performing PCA inverse transform on the image blocks to the time domain, restoring all image blocks to an image matrix, and finally obtaining a dark-field confocal subsurface defect denoised image with preserved details. This invention does not require manual input parameters and can effectively preserve the detailed information of the subsurface defect structure and weak subsurface defect signals while eliminating background noise.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and more specifically to an adaptive detail-preserving noise reduction method based on truncated singular values ​​and principal component analysis. Background Technology

[0002] Image denoising technology belongs to the field of image processing. Dark field confocal images are inevitably affected by noise from the substrate and system during acquisition, transmission and storage. The introduction of noise will reduce the signal-to-noise ratio of dark field confocal images, and may even obscure the detailed information of subsurface defect structures and weak subsurface defect scattering signals.

[0003] Subsurface defects at the micro- and nano-scale typically contain rich high-frequency information. Conventional filtering-based noise reduction methods, while eliminating noise, also lead to the loss of high-frequency information from subsurface defects. How to remove as much noise as possible while preserving the detailed information of subsurface defects is one of the problems that need to be solved in dark field confocal image processing.

[0004] In recent years, the nonlocal self-similarity prior of images has been widely used in denoising algorithms. The low-rank denoising algorithm based on nonlocal theory and low-rank theory groups similar blocks in the image to form an image block group matrix; then, singular value decomposition is performed on each combined matrix, and large numerical singular values ​​are retained to perform low-rank approximation of the matrix, thereby obtaining a good denoising effect.

[0005] Truncated singular value algorithm is a denoising method based on the aforementioned low-rank theory. Truncated singular value denoising belongs to the hard thresholding denoising method. The main limitation of this method is that the rank of the matrix must be input when executing the algorithm. However, the setting of the rank in traditional truncated singular value algorithm is heavily dependent on empirical values. Too low or too high a rank will lead to loss of image details or noise residue, respectively. Automatic determination of the image rank is the key to realizing an adaptive truncated singular value algorithm.

[0006] Therefore, how to provide an adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides an adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis. The purpose is to solve the problem that traditional denoising algorithms are prone to losing detail information and weak defect signals when processing dark field confocal subsurface defect images, and the denoised images cannot meet engineering needs. Compared with traditional filtering-based algorithms, this algorithm does not require manual input parameters and can better preserve the detail information of subsurface defect structures and weak subsurface defect signals while eliminating background noise.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis includes the following steps:

[0010] S1. Perform noise estimation on the global subsurface defect image to obtain the eigenvalues ​​of the global noise matrix;

[0011] S2. Divide the original noisy image into overlapping image blocks, and use an adaptive clustering method to obtain different block group matrices X composed of similar image blocks. φ Each block group matrix corresponds to a feature classification.

[0012] S3. Perform adaptive truncation singular value denoising on each type of image patch matrix to obtain a low-noise clustering matrix:

[0013] when When r < i ≤ M, the block group matrix X φ It can be approximately decomposed into two parts: in The image component dominated by noise; It is the signal-dominated image component; all components greater than λ n,min The number of singular values ​​is approximately equal to X. φ The rank r; obtained using Gaussian noise estimation method By combining a noise estimation algorithm, the rank r of the matrix is ​​adaptively obtained;

[0014] X φ Clustering, to obtain the clustering matrix Where j is the number of clusters after clustering, j = 1, ..., K;

[0015] Perform singular value decomposition on each cluster, retaining values ​​greater than 1 in each cluster. The singular values ​​are used to obtain a signal-dominated image patch matrix containing a small amount of noise. Perform adaptive truncation and singular value hard thresholding for noisy images;

[0016] S4. Adaptive principal component analysis is used to process the low-noise clustering matrix to obtain image patches.

[0017] S5. Image patch Perform principal component analysis and inverse transform to the time domain, then analyze all image patches. The image matrix is ​​restored, and finally a dark-field confocal subsurface defect denoising image with preserved details is obtained.

[0018] Preferably, the specific content of S2 includes:

[0019] S21. Divide the image into L partitions of size M = d. 2Overlapping image patches, each denoted as x i , using X φ =[x1,…,x k ,…,x L ] represents a block group matrix containing L image patches, where X φ ∈R M×L The number of image blocks L = (a-d+1)(b-d+1), where a and b represent the height and width of the image, respectively.

[0020] S22. Divide the image patches into four categories based on the color features, texture features, shape features, and spatial relationship features of the image, so that each feature cluster after clustering corresponds to one image feature;

[0021] S23. Each feature cluster in the initially divided four feature cluster matrices is divided using over-clustering and iterative merging.

[0022] Preferably, the specific details of the partitioning process in S23 using clustering and iterative merging include:

[0023] (1) Divide each feature cluster into... There are several clusters, where floor(·) represents the floor function, and L j0 This represents the number of block vectors in the j0th feature cluster matrix;

[0024] (2) After clustering, perform iterative merging: Set a merging threshold T, if the distance between any two classes is... Then these two classes are merged, where ||·||2 represents the l2 norm, and the vector... and This represents the mean vector of two clustered image patch groups;

[0025] (3) The iteration ends when the number of image block groups no longer changes.

[0026] Preferably, in S3, X φ The specific method of decomposition is as follows:

[0027]

[0028] The image contaminated by noise is considered as a linear combination of a low-noise image and noise, with the block group matrix X. φ It is broken down into two parts: and in The image component dominated by noise; It is the signal-dominated image component.

[0029] Preferably, the specific content of S4 includes:

[0030] Even after adaptive singular value hard thresholding denoising, the signal-dominated image patch matrix is ​​still a noisy image, and its image model is represented as follows:

[0031] in, Let j be the matrix of noise-free image patches. N j The noise is Gaussian noise in the j-th class image patch group matrix.

[0032] matrix Mean μ of each row q for:

[0033]

[0034] Where q = 1, 2, ..., l, for the matrix Each row is processed centrally:

[0035] The low-noise image after centering is represented as:

[0036] Since the mean of Gaussian noise is zero and it is independent of the noise-free image, the centered noisy image model is obtained as follows:

[0037] Calculate known noisy images covariance matrix To obtain the covariance matrix Thus, a noise-free image is obtained. Orthogonal transformation matrix Will Substitute noisy image This achieves signal-to-noise separation:

[0038]

[0039] calculate Covariance matrix:

[0040]

[0041] in, Represents the decorrelation matrix The covariance matrix, Represents the noise transformation matrix N Y The covariance matrix;

[0042] Using the coefficient shrinkage method to Noise reduction processing:

[0043]

[0044]

[0045] in, express The qth line, w q Indicates the weighting coefficient. express The value of the qth row after being shrunk by the weighting coefficients; express eigenvalue diagonal matrix The element in the q-th row and q-th column; N represents j eigenvalue diagonal matrix The element in the q-th row and q-th column is obtained through a noise estimation algorithm.

[0046] In areas with high noise levels The value is greater than At this time w q The value approaches zero, using w q The obtained principal components are scaled; the noise-dominant principal components are scaled down and discarded, while the signal-dominant principal components are retained, thus achieving... Adaptive noise reduction.

[0047] Preferably, in S5, the image block... The specific content of principal component analysis inverse transform to the time domain includes:

[0048]

[0049] in If it is a standard orthogonal matrix, then therefore but:

[0050]

[0051]

[0052] As can be seen from the above technical solution, compared with the prior art, the present invention discloses an adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis. The present invention can overcome the problems of traditional truncated singular value algorithms relying on experience to blindly judge the truncating operator, resulting in noise residue when the truncating operator is too large, or loss of detail information when the truncating operator is too small. By estimating noise, the truncating operator is adaptively judged, and the image is coarsely denoised using hard thresholding of truncated singular values ​​to avoid loss of image detail information. The coarsely denoised image is finely denoised using adaptive shrinking of principal component analysis coefficients. While achieving adaptive denoising and reducing noise residue, the image detail information can be preserved to the greatest extent. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0054] Figure 1 The flowchart provided for the adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis of the present invention;

[0055] Figure 2 This diagram illustrates a comparison of denoising results obtained using Wiener filtering, wavelet filtering, and an adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis, as provided in embodiments of the present invention. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] This invention discloses an adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis, such as... Figure 1 As shown, the specific steps include:

[0058] An adaptive detail-preserving denoising method based on truncated singular values ​​and principal component analysis includes the following steps:

[0059] S1. Perform noise estimation on the global subsurface defect image to obtain the eigenvalues ​​of the global noise matrix;

[0060] S2. Divide the original noisy image into overlapping image blocks, and use an adaptive clustering method to obtain different block group matrices X composed of similar image blocks. φ Each block group matrix corresponds to a feature classification.

[0061] S3. Perform adaptive truncation singular value denoising on each type of image patch matrix to obtain a low-noise clustering matrix:

[0062] when When r < i ≤ M, the block group matrix X φ It can be approximately decomposed into two parts: and in For image components dominated by noise, hard thresholding can be used to remove them directly by selecting an appropriate truncation operator. This is the signal-dominated image component, mixed with a small amount of noise. To preserve image details, fine noise reduction using soft thresholding is necessary; all components greater than λ... n,min The number of singular values ​​is approximately equal to X. φ The rank r; obtained using Gaussian noise estimation method Therefore, by combining the noise estimation algorithm, the rank r of the matrix can be obtained adaptively.

[0063] X φ Clustering, to obtain the clustering matrix Where j is the number of clusters after clustering, j = 1, ..., K;

[0064] Perform singular value decomposition on each cluster, retaining values ​​greater than 1 in each cluster. The singular values ​​are used to obtain a signal-dominated image patch matrix containing a small amount of noise. Perform adaptive truncation and singular value hard thresholding for noisy images;

[0065] S4. Adaptive principal component analysis is used to process the low-noise clustering matrix to obtain image patches.

[0066] S5. Image patch Perform principal component analysis and inverse transform to the time domain, then analyze all image patches. The image matrix is ​​restored, and finally a dark-field confocal subsurface defect denoising image with preserved details is obtained.

[0067] It should be noted that

[0068] In S1, noise estimation is performed on the image to be denoised to avoid blindly inputting the noise variance, which affects the accuracy of matrix rank estimation, leading to residual noise or loss of detail information in the denoised image and increasing the complexity of the algorithm. In S3, adaptive truncated singular value denoising is performed on the matrix of each type of image block group. Traditional truncated singular value denoising algorithms require manual judgment of the matrix rank based on empirical values. Too low a matrix rank will lead to loss of detail information, while too high a matrix rank will lead to residual noise. Moreover, the rank is set to a fixed value, but the rank of different images is different. A fixed rank will reduce the denoising effect. The adaptive truncated singular value algorithm can adaptively judge the rank of the matrix for different images based on the noise estimate, avoiding the denoising defects caused by a fixed rank.

[0069] To further implement the above technical solution, the specific content of S2 includes:

[0070] S21. Divide the image into L partitions of size M = d. 2Overlapping image patches, each denoted as x i , using X φ =[x1,…,x k ,…,x L ] represents a block group matrix containing L image patches, where X φ ∈R M×L The number of image blocks L = (a-d+1)(b-d+1), where a and b represent the height and width of the image, respectively.

[0071] S22. Divide the image patches into four categories based on the color features, texture features, shape features, and spatial relationship features of the image, so that each feature cluster after clustering corresponds to one image feature;

[0072] S23. Each feature cluster in the initially divided four feature cluster matrices is divided using over-clustering and iterative merging.

[0073] To further implement the above technical solution, the specific details of the partitioning process in S23, which uses over-clustering and iterative merging, include:

[0074] (1) Divide each feature cluster into... There are several clusters, where floor(·) represents the floor function, and L j0 This represents the number of block vectors in the j0th feature cluster matrix;

[0075] (2) After clustering, perform iterative merging: Set a merging threshold T. For images containing Gaussian noise, T is generally set to T = 16σ. 2

[93] The value is taken as follows, where σ is the global noise variance estimated using the noise estimation algorithm; if the distance between any two classes is... Then these two classes are merged, where ||·||2 represents the l2 norm, and the vector... and This represents the mean vector of two clustered image patch groups;

[0076] (3) The iteration ends when the number of image block groups no longer changes.

[0077] To further implement the above technical solution, S3 includes X... φ The specific method of decomposition is as follows:

[0078]

[0079] The image contaminated by noise is considered as a linear combination of a low-noise image and noise, with the block group matrix X. φ It is broken down into two parts: and in The image component dominated by noise; It is the signal-dominated image component.

[0080] To further implement the above technical solution, the specific content of S4 includes:

[0081] Even after adaptive singular value hard thresholding denoising, the signal-dominated image patch matrix is ​​still a noisy image, and its image model is represented as follows:

[0082] in, Let j be the matrix of noise-free image patches. N j The noise is Gaussian noise in the j-th class image patch group matrix.

[0083] matrix Mean μ of each row q for:

[0084]

[0085] Where q = 1, 2, ..., l, for the matrix Each row is processed centrally:

[0086] The low-noise image after centering is represented as:

[0087] Since the mean of Gaussian noise is zero and it is independent of the noise-free image, the centered noisy image model is obtained as follows:

[0088] Calculate known noisy images covariance matrix To obtain the covariance matrix Thus, a noise-free image is obtained. Orthogonal transformation matrix Will Substitute noisy image This achieves signal-to-noise separation:

[0089]

[0090] calculate Covariance matrix:

[0091]

[0092] in, Represents the decorrelation matrix The covariance matrix, Represents the noise transformation matrix N Y The covariance matrix;

[0093] Using the coefficient shrinkage method to Noise reduction processing:

[0094]

[0095] in, express The qth line, w q Indicates the weighting coefficient. express The value of the qth row after being shrunk by the weighting coefficients;

[0096] To achieve adaptive selection of the number of principal components, a weighting coefficient w is designed. q :

[0097]

[0098] express eigenvalue diagonal matrix The element in the q-th row and q-th column; N represents j eigenvalue diagonal matrix The element in the q-th row and q-th column is obtained through a noise estimation algorithm.

[0099] In areas with high noise levels The value is greater than At this time w q The value approaches zero, using w q The obtained principal components are scaled; the noise-dominant principal components are scaled down and discarded, while the signal-dominant principal components are retained, thus achieving... Adaptive noise reduction.

[0100] It should be noted that:

[0101] Principal component analysis (PCA) is a soft-threshold denoising method. Its main limitation lies in determining the number of principal components. Insufficient retention of principal components leads to the loss of effective information, while excessive retention leads to information redundancy. How to reasonably retain principal components is a problem that PCA algorithms need to solve.

[0102] The method described in this invention utilizes adaptive principal component analysis to process the signal-dominated low-noise clustering matrix after adaptive singular value truncation hard thresholding. During the principal component analysis process, a noise estimation algorithm is used to estimate the noise in the signal-dominated low-noise matrix. The noise estimate can be used to adaptively calculate scaling weight coefficients for different images. This effectively solves the problems of insufficient retention of principal components leading to loss of effective information and excessive retention of principal components leading to information redundancy in principal component analysis. It achieves further refined noise reduction of signal-dominated images and avoids noise residue or loss of detail caused by manually selecting principal components.

[0103] To further implement the above technical solution, image blocks are processed in S5. The specific content of principal component analysis inverse transform to the time domain includes:

[0104]

[0105] in If it is a standard orthogonal matrix, then therefore but:

[0106]

[0107] The original matrix was centered during the PCA forward transformation, meaning the mean μ was subtracted from each row. q After performing the inverse transformation, the mean of each row needs to be added, as shown in the following formula:

[0108] This completes all the noise reduction steps.

[0109] Then, all image blocks are restored into an image matrix, and finally, a dark-field confocal subsurface defect noise-reduced image with preserved details is obtained.

[0110] The invention will be further illustrated below through specific experiments:

[0111] Denoising was performed using Wiener filtering, wavelet filtering, and adaptive detail-preserving denoising methods that truncate singular values ​​and principal component analysis, respectively. The quantitative comparison of the denoising results is shown in Table 1.

[0112] Table 1

[0113]

[0114]

[0115] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0116] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An adaptive detail-preserving denoising method based on truncated singular value and principal component analysis, characterized in that, The method comprises the following steps: S1. Noise estimation is performed on the global subsurface defect image to obtain eigenvalues of a global noise matrix; S2. The original noise image is divided into mutually overlapping image blocks, and an adaptive clustering method is used to obtain different block group matrices X composed of similar image blocks φ Each block group matrix corresponds to a feature category respectively; S3. Each of the image block group matrices is subjected to adaptive truncated singular value denoising to obtain a low-noise clustering matrix: When where r < i < M, the block matrix X φ is approximately decomposed into two parts: and where is the noise-dominant image component; is the signal-dominant image component; the number of singular values greater than λ n,min is approximately equal to the rank r of X φ . The Gaussian noise estimation method is used to obtain In combination with the noise estimation algorithm, the rank r of the matrix is adaptively obtained. X φ clustering matrix where j is the number of clusters after clustering, j = 1, …, K. Each cluster is singular value decomposed respectively, and singular values greater than in each cluster are reserved to obtain a signal dominant image block group matrix containing a small amount of noise The adaptive truncated singular value hard threshold denoising of the noise image is completed; S4. processing the low-noise clustering matrix using adaptive principal component analysis to obtain an image block S5. performing principal component analysis inverse transform to time domain on the image blocks to restore all the image blocks into image matrix, and finally obtain dark-field confocal subsurface defect denoising image with details preserved.​ The specific content of S4 comprises: The image block group matrix dominated by the signal after adaptive truncated singular value hard threshold denoising is still a noisy image, and the image model is expressed as wherein, is the jth set of noise-free image block matrices, N j is the jth set of Gaussian noise of image block matrices, matrix the mean μ of each row q is: where q = 1, 2,..., l, and the matrix Each row is centered: The low-noise image after the centering process is represented as Since the mean of the Gaussian noise is zero and independent of the noise-free image, the centralized noise image model is obtained as by calculating the covariance matrix of the known noisy image then signal and noise separation is achieved:​​​​​​ Computing the covariance matrix: wherein denotes the covariance matrix of the decorrelation matrix denotes the covariance matrix of the decorrelation matrix denotes the covariance matrix of the noise transform matrix N Y denotes the covariance matrix of the noise transform matrix N The coefficient shrinkage method is used to perform noise reduction processing on the following equation: perform noise reduction processing: wherein, denotes the qth row of q denotes a weight coefficient, denotes a value of the qth row of after weight coefficient shrinkage; denotes an eigenvalue diagonal matrix of an element in the qth row and the qth column; denotes N j an element in the qth row and the qth column of the eigenvalue diagonal matrix obtained by a noise estimation algorithm In the area where the noise intensity is large, the value of At this time, w q the value of w q is close to zero, and the obtained principal component is scaled, the noise-dominant principal component is reduced and discarded, and the signal-dominant principal component is retained, thereby realizing adaptive noise reduction of .

2. The adaptive detail-preserving denoising method based on truncated singular value and principal component analysis according to claim 1, characterized in that, The specific content of S2 comprises: S21. Divide the image into L overlapped image blocks of size M = d 2 , each image block is denoted as x i , and the block group matrix containing L image blocks is denoted as X φ = [x1,..., x k ,..., x L ], where X φ ∈ R M×L , the number of image blocks L = (a - d + 1)(b - d + 1), a and b represent the height and width of the image, respectively; S22. The image blocks are divided into four categories according to color features, texture features, shape features and spatial relationship features of the image, so that each of the clustered feature clusters corresponds to one image feature; S23. Each of the four feature cluster matrices after the preliminary division is divided by using the over-clustering and iterative merging manner.

3. The method of claim 2, wherein the method is based on a truncated singular value decomposition and principal component analysis adaptive detail-preserving denoising method. The specific content of the over-clustering and iterative merging manner for division in S23 comprises: (1) each feature cluster is re-divided into clusters, where floor( ) denotes a floor function, L j0 represents the number of block vectors in the j0th feature cluster matrix; (2) After over-clustering, iterative merging is performed: set a merging threshold T, if the distance between any two clusters is then the two clusters are merged, where ||·||2 denotes the l2 norm, and the vectors and represent the mean vectors of the two groups of clustered image blocks; (3) When the number of image block groups no longer changes, the iteration ends.

4. The method of claim 1, wherein the method is characterized by, S3 in X φ The specific method of decomposition is: The image contaminated by noise is considered as a linear combination of a low noise image and noise, the block group matrix X φ is decomposed into two parts: and where is the noise dominant image component; is the signal dominant image component.

5. The method of claim 1, wherein the method is characterized by, S5 in the image block The details of the inverse principal component analysis transform into the time domain include: wherein is a standard orthogonal matrix, then Thus then:

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