An image denoising algorithm based on superpixel clustering PCA

Abstract

An image denoising algorithm based on superpixel clustering PCA, which relates to an image denoising algorithm. The present invention aims to solve the problem that many current PCA-based denoising algorithms only consider energy transformation between dimensions and ignore energy transformation within dimensions, resulting in insufficient denoising effect. Due to the low signal-to-noise ratio and weak signal characteristics of dark-field confocal images, the algorithm is difficult to meet the engineering requirements of dark-field confocal image denoising. The present invention performs superpixel segmentation on the image through the SLIC method to reduce the computational complexity; collects similar image blocks through adaptive clustering of noise level-related parameters, thereby obtaining a good ability to retain image detail structure; removes the noise-dominated dimension through hard threshold dimension selection based on eigenvalues, retains the signal-dominant dimension; and utilizes intra-dimensional suboptimal Wiener filtering to obtain better denoising effect. The present invention belongs to the field of image processing technology.

Description

Technical Field

[0001] The invention relates to an image noise reduction algorithm and belongs to the technical field of image processing. Background Art

[0002] Dark-field confocal microscopy with high signal-to-noise ratio and high contrast imaging of sub-surface defects of optical components is very important for studying the systematic characterization and formation mechanism of sub-surface defects. However, the introduction of noise will reduce the signal-to-noise ratio of the image, and even mask the weak scattering signals of sub-surface defects, making it impossible to show the structural details, thus affecting the detection of sub-surface defects. Therefore, it is necessary to reduce the noise of dark-field confocal images of sub-surface defects and improve their signal-to-noise ratio. PCA is a commonly used data dimensionality reduction method and a classic decorrelation technique in statistical signal processing. By converting the original data set to the PCA domain and retaining only a few of the most important principal components, noise and trivial information can be removed. At present, many PCA-based denoising algorithms only consider the energy transformation between dimensions and ignore the energy transformation within dimensions, and the denoising effect is insufficient. Due to the low signal-to-noise ratio and weak signal characteristics of dark-field confocal images, the algorithm is difficult to meet the engineering requirements of dark-field confocal image denoising. Summary of the invention

[0003] The present invention aims to solve the problem that many current PCA-based denoising algorithms only consider the energy transformation between dimensions but ignore the energy transformation within dimensions, resulting in insufficient denoising effect. Due to the low signal-to-noise ratio and weak signal of dark-field confocal images, the algorithms are difficult to meet the engineering needs of dark-field confocal image denoising. Therefore, an image denoising algorithm based on superpixel clustering PCA is proposed.

[0004] The technical solution adopted by the present invention to solve the above-mentioned problem is: the steps of the present invention include:

[0005] Step 1: Input a dark field confocal sub-surface defect image X with noise;

[0006] Step 2: Use the SLIC method to perform superpixel segmentation on image X, and combine similar pixels in the image to form a superpixel set {R1,,...,R N};

[0007] Step 3: Adaptively cluster similar image blocks in each superpixel to obtain similar block clusters;

[0008] Step 4: Aggregate each superpixel to obtain the final denoised image X out ;

[0009] Step 5: Output the noise-reduced dark field confocal sub-surface defect image X out .

[0010] Furthermore, in step 3, the step of adaptively clustering similar image blocks in each superpixel to obtain similar block clusters includes:

[0011] Step 1: When d(x j ,x k ) is less than or equal to the threshold value related to the noise level, clustering and normalization are performed to obtain clustering

[0012] Step 2: Use PCA to denoise each cluster;

[0013] Step 3: Combine clustering to obtain denoised super-image

[0014] Furthermore, in step 1, d(x j ,x k ) is the Euclidean distance, which is used as a similarity measure:

[0015]

[0016] In the above formula, is the image patch centered at pixel position k, d(x j ,x k ) is smaller, indicating that the image block x j and x k The more similar.

[0017] Furthermore, PCA is used to denoise each cluster in step 2:

[0018] Step (1), perform PCA transformation;

[0019] Step (2), hard threshold dimension selection: remove singular values ​​less than The dimension of X r =U r P r ;

[0020] Step (3), for each selected dimension: estimate the filter parameter h using a local polynomial approximation;

[0021] Step (4): For each selected dimension: perform suboptimal Wiener filtering to obtain

[0022] Step (5): inverse PCA transformation.

[0023] The beneficial effects of the present invention are:

[0024] 1. The present invention uses the SLIC method to perform superpixel segmentation on the image to reduce the computational complexity; collects similar image blocks through adaptive clustering of noise level related parameters, thereby obtaining a good ability to retain image detail structure; removes the noise-dominated dimension through hard threshold dimension selection based on eigenvalues, and retains the signal-dominated dimension; and uses intra-dimensional suboptimal Wiener filtering to obtain better noise reduction effect;

[0025] 2. Through bright field confocal image simulation experiments, it can be seen that the signal-to-noise ratio improvement factor of the image denoised by the proposed algorithm is 13.47 compared with the noisy image, and the present invention has good performance in MSE, PSNR, SSIM and FSIM, which is better than the NLM algorithm, KSVD algorithm and LPG-PCA algorithm;

[0026] 3. The present invention verifies the engineering application value of the algorithm in this paper through dark field confocal image experiments. The algorithm in this paper performs best in terms of SNR and NIDQA scores.

[0027] 4. The present invention can retain image detail information while having good noise reduction performance, providing a high signal-to-noise ratio image for image enhancement. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of the present invention. DETAILED DESCRIPTION

[0029] Specific implementation method 1: Combination Figure 1 The present embodiment is described. The steps of an image denoising algorithm based on superpixel clustering PCA described in the present embodiment include:

[0030] Step 1: Input a dark field confocal sub-surface defect image X with noise;

[0031] Step 2: Use the SLIC method to perform superpixel segmentation on image X, and combine similar pixels in the image to form a superpixel set {R1,,...,R N};

[0032] Step 3: Adaptively cluster similar image blocks in each superpixel to obtain similar block clusters;

[0033] Step 4: Aggregate each superpixel to obtain the final denoised image X out ;

[0034] Step 5: Output the noise-reduced dark field confocal sub-surface defect image X out .

[0035] Specific implementation method 2: Combination Figure 1To illustrate this embodiment, in step 3 of the image denoising algorithm based on superpixel clustering PCA described in this embodiment, the step of adaptively clustering similar image blocks in each superpixel to obtain similar block clusters includes:

[0036] Step 1: When d(x j ,x k ) is less than or equal to the threshold value related to the noise level, clustering and normalization are performed to obtain clustering

[0037] Step 2: Use PCA to denoise each cluster;

[0038] Step 3: Combine clustering to obtain denoised super-image

[0039] Specific implementation method three: Combination Figure 1 In this embodiment, the image denoising algorithm based on superpixel clustering PCA described in step 1 is described as follows: j ,x k ) is the Euclidean distance, which is used as a similarity measure:

[0040]

[0041] In the above formula, is the image patch centered at pixel position k, d(x j ,x k ) is smaller, indicating that the image block x j and x k The more similar.

[0042] Specific implementation method four: Combination Figure 1 This embodiment is described. In step 2 of the image denoising algorithm based on superpixel clustering PCA described in this embodiment, PCA is used to denoise each cluster:

[0043] Step (1), perform PCA transformation;

[0044] Step (2), hard threshold dimension selection: remove singular values ​​less than The dimension of X r =U r P r ;

[0045] Step (3), for each selected dimension: estimate the filter parameter h using a local polynomial approximation;

[0046] Step (4): For each selected dimension: perform suboptimal Wiener filtering to obtain

[0047] Step (5): inverse PCA transformation.

[0048] This implementation adopts a two-stage texture change adaptive approximation strategy to achieve texture-preserving denoising performance. First, dimension selection and low-rank approximation are implemented through a hard threshold shrinkage function based on eigenvalues, thereby selectively retaining the energy change of the dominant dimension of the signal. Second, the coefficient adaptive suboptimal Wiener filter of the local estimated filter parameters is used to adaptively denoise the main dimension of each signal to protect the texture change in the next dimension:

[0049] Dimensional Selection of Interdimensional Energy Changes

[0050] Discard the noise-dominated dimensions through dimension selection to reduce computational cost and improve denoising performance; consider the normalized clustering matrix with noise Then there is in is noise-free data, N=[n0,......,n R-1 ] is each column vector n i ∈N(0,σ 2 I), where I is the identity matrix, is transformed into PCA according to the singular value decomposition theory:

[0051]

[0052] Among them U X and V X is an orthogonal matrix, L X is a diagonal matrix with the diagonal elements arranged in descending order, assuming and They are singular values, u i 、v i 、u i,y 、v i,y are singular value vectors, L is the number of dimensions selected by the hard threshold, then:

[0053]

[0054]

[0055] The hard threshold dimension selection of this method is based on the Gaussian spike population model, assuming that the constant γ = R / M, let R→∞ and but:

[0056]

[0057] where ρ is a real-valued function, and the Gaussian peaked population model surface has an eigenvalue of the dominant dimension of the noise for a normal-sized clustering matrix of approximately n+ Next, consider the eigenvalue close to λ n+ The dimension of still contains noise, set the correction coefficient ω to estimate the rank r:

[0058]

[0059] Setting a reasonable ω value to obtain good denoising performance, the low-rank approximation is:

[0060]

[0061] In addition to hard thresholding, other shrinkage functions such as soft thresholding can be used to suppress noise in the dimensionality reduction data. The hard thresholding is chosen because it does not change the value of the coefficients and can effectively keep the local properties of the signal unchanged in the PCA domain, ensuring that the edges and structures of the image are preserved.

[0062] Intra-dimensional texture adaptive filtering

[0063] X obtained by hard thresholding r =U r P r , where U r =[u x,1 u x,2 ...u x,r ], P r It is composed of the dominant dimension of the corresponding signal in the PCA transform domain:

[0064] P r =[p1p2...p r ] T ,

[0065] in, is the selected PCA dimension, where 1≤i≤r;

[0066] The local polynomial approximation of point-by-point adaptive estimation combined with the confidence interval intersection rule method is used to extract p i =[p i,1 p i,2 ...p i,R ], which is represented as a signal sequence x(n)=p containing R observation points i,n , the variance of x(n) is And x(n)=y(n)+v(n), where v(n) is the variance Var[v(n)]=σ 2 Gaussian noise;

[0067] In the standard local polynomial approximation, the loss function is:

[0068]

[0069] Where n is the position of the window center, m is the order, and ρ h(n) = ρ(n / h) / h is the window function, h is the window size, and the maximum window size is adaptively determined using the confidence interval intersection rule, so that the local polynomial approximation of the signal is better. For the original signal without noise and smoothness, this method can obtain the best signal recovery quality. However, since the signal composed of coefficients in the PCA transform domain is not necessarily smooth, in order to avoid over-smoothing results, this method is not used directly on the signal, but h is calculated by this method to estimate the window size parameter required for suboptimal Wiener filtering. Let m = 1, assuming that a window signal is x(n s )=y(n s )+v(n s ), and 1≤s≤N0, where N0 is the number of signals in the window, if x c (n) is the window center, then the correlation coefficient is:

[0070]

[0071] x c (n) Using the suboptimal Wiener filter, we have:

[0072]

[0073] Where R v is the noise v c The correlation coefficient of (n), α is the attenuation coefficient, is obtained by solving the minimization problem:

[0074]

[0075] subject to 0<α<1,

[0076] Where β is a parameter that determines the relative importance between signal distortion and noise suppression. When β decreases, the importance of suppressing noise is greater than suppressing signal distortion. The suboptimal Wiener filter is used to process each p i , and get the corresponding processing results You can get The denoised clusters are obtained through inverse PCA transformation:

[0077] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. An image denoising method based on superpixel clustering PCA, characterized in that: A two-stage texture change adaptive approximation strategy is adopted to achieve texture-preserving denoising performance. First, dimension selection and low-rank approximation are achieved through a hard threshold shrinkage function based on eigenvalues, thereby selectively retaining the energy change of the dominant dimension of the signal. Secondly, the coefficient adaptive suboptimal Wiener filter of the local estimated filter parameter is used to adaptively denoise the main dimension of each signal to protect the texture change in the next dimension. The steps of the image denoising method based on superpixel clustering PCA include: Step 1: Input a dark field confocal sub-surface defect image X with noise; Step 2: Use the SLIC method to perform superpixel segmentation on image X, and combine similar pixels in the image to form a superpixel set {R1,......,R N }; Step 3: Adaptively cluster similar image blocks in each superpixel to obtain similar block clusters; the specific steps include: Step 1: When d(x j ,x k ) is less than or equal to a threshold value related to the noise level, clustering and normalization are performed to obtain clusters; Step 2: Use PCA to denoise each cluster; specifically: Step (1), perform PCA transformation; Step (2), hard threshold dimension selection: remove singular values ​​less than Dimensions; Step (3), for each selected dimension: estimate the filter parameter h using a local polynomial approximation; Step (4), for each selected dimension: perform suboptimal Wiener filtering; Step (5), inverse PCA transformation; Step 3: Combine clustering to obtain denoised superpixels d(x j ,x k ) is the Euclidean distance, which is used as a similarity measure: In the above formula, is the image patch centered at pixel position k, d(x j ,x k ) is smaller, indicating that the image block x j and x k The more similar; Step 4, aggregating each superpixel to obtain the final denoised dark field confocal sub-surface defect image; Step 5: Output the noise-reduced dark field confocal sub-surface defect image; n+ represents the eigenvalue approximation value; ω represents the correction coefficient.

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