A Single-Image Noise Estimation Algorithm Based on Pixel-Level Low-Rank Low-Texture Patch and Principal Component Analysis
Abstract
:1. Introduction
2. Method
2.1. Formulation
2.2. Proposed Method
2.2.1. An Adaptive Clustering Method Based on Dichotomy Merge
Algorithm 1: Adaptive clustering algorithm based on dichotomy merge |
Input: Noisy image Y, standard deviation of noise σ, size of image batch c, maximum number of iterations K. |
Output: Low-rank sub-image block group. |
Steps: |
1. The noise image is divided into blocks with the size of c × c, and the adjacent image blocks are only different by one row or one column; |
2. While the class center does not change or the number of iterations k = K |
For each class |
1. The mean and variance of each image block in the class are calculated and combined as the centroid judgment factor; |
2. The two image blocks with the largest difference in centroid judgment factor are selected as the two initial class centers; |
3. The K-means algorithm is used for clustering, and the class center of each class is calculated; |
End for |
4. The distance between classes is calculated, and the merging threshold is used to determine whether the class needs merging; |
5. k = k + 1; |
End while |
2.2.2. Construction Method of Pixel-Level Low-Rank Image Subblock Matrix
Algorithm 2: Construction method of pixel-level low-rank image subblock matrix |
Input: Initial low-rank image subblock matrix Yk, standard deviation of noise σ, minimum number of similar rows N, zoom factor η |
Output: Pixel-level low-rank image subblock matrix |
Steps: |
1. The row with the smallest variance in the initial low-rank image subblock matrix is calculated as the reference sub-image block vector; |
2. For all row vectors of the initial low-rank image subblock matrix |
1. Calculate the similarity measure function: ; |
2. Calculate the threshold: ; |
3. If , the row is kept as a similar row; End for |
3. If the number of rows of the output pixel-level low-rank image sub-block matrix is less than N, increase the scaling factor η = η + 0.01 and go to step 2; |
4. Output the pixel-level low-rank image subblock matrix |
2.2.3. Low-Texture Subblock Selection Method Based on Gradient Covariance
2.2.4. Eigenvalue Selection Method
2.3. Proposed Algorithm
Algorithm 3: Our method |
Input: original noise image Y, scaling factor η, scaling factor η1, scaling factor η2, minimum number of similar rows N, image block size c, maximum number of iterations K, error tolerance parameter dlt, confidence factor δ. |
Output: estimated standard deviation of noise. |
Steps: |
1. Calculate the initial standard deviation σ0 of noise using the algorithm in [38]; |
2. Construct the initial low-rank sub-image matrix Yl = {y1,y2…yl} ∈ Rm×l using algorithm 1; |
3. Calculate the threshold , select the sub-image with the minimum standard deviation as the reference sub-image vector, use the Euclidean distance as the criterion, retain the sub-image blocks whose Euclidean distance is less than the threshold in Yl as the new low-rank sub-image matrix Yk = [y1, y2… yk] ∈ Rm×k, and if the least number of elements in the low-rank matrix is , run step 4, otherwise η1 = η1 + 0.01, and then rerun step 3; |
4. Use Algorithm 2 to construct pixel-level low-rank image subblocks ∈ Riq×k; |
5. For the ith image subblock, I = 1:k |
|
|
|
End for. Output the pixel-level low-rank low-texture sub-image matrix Ywp ∈ Riq×wp; |
6. If iq × wp < n, then go back to step 3; |
7. If iq × wp < n and all sub-blocks participate in the calculation, increase the texture intensity threshold and return to step 5; |
8. Perform SVD for Ywp; |
9. Through the judgment criteria, and , obtain the number of eigenvalues, ip and io; |
10. Obtain |
11. Calculate the standard deviation of the noise |
3. Experiment
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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σ | c | δ | dlt | η | η1 | η2 | N |
---|---|---|---|---|---|---|---|
≤15 | 10 | 1-10−6 | 0.02 | 0.93 | 3 | 1.2 | 70% |
≤35 | 10 | 1-10−6 | 0.02 | 0.93 | 3 | 1.2 | 70% |
≤90 | 10 | 1-10−6 | 0.1 | 0.99 | 3 | 1.2 | 70% |
≤120 | 10 | 1-10−6 | 0.1 | 0.99 | 3 | 1.2 | 70% |
≤150 | 10 | 1-10−6 | 0.1 | 1 | 3 | 1.2 | 70% |
≤200 | 10 | 1-10−6 | 0.1 | 1.01 | 3 | 1.2 | 70% |
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Li, Y.; Liu, C.; You, X.; Liu, J. A Single-Image Noise Estimation Algorithm Based on Pixel-Level Low-Rank Low-Texture Patch and Principal Component Analysis. Sensors 2022, 22, 8899. https://doi.org/10.3390/s22228899
Li Y, Liu C, You X, Liu J. A Single-Image Noise Estimation Algorithm Based on Pixel-Level Low-Rank Low-Texture Patch and Principal Component Analysis. Sensors. 2022; 22(22):8899. https://doi.org/10.3390/s22228899
Chicago/Turabian StyleLi, Yong, Chenguang Liu, Xiaoyu You, and Jian Liu. 2022. "A Single-Image Noise Estimation Algorithm Based on Pixel-Level Low-Rank Low-Texture Patch and Principal Component Analysis" Sensors 22, no. 22: 8899. https://doi.org/10.3390/s22228899