![]() Ghosh S Mandal A Chaudhury K Pruned non-local means IET Image Processing 2017 11 317 323 10.1049/iet-ipr.2016.0331 Google Scholar Cross Ref.Denoising color images by reduced quaternion matrix singular value decomposition Multidimensional Systems and Signal Processing 210.1007/s1104-x 1435.94014 Google Scholar Digital Library Frosio I Kautz J Statistical nearest neighbors for image denoising IEEE Transactions on Image Processing 210.1109/TIP.2018.2869685 1409.94156 Google Scholar Digital Library.Duval V Aujol JF Gousseau Y A bias-variance approach for the nonlocal means SIAM Journal on Imaging Sciences 210.1137/100790902 1219.94004 Google Scholar Digital Library.Patch redundancy in images: A statistical testing framework and some applications SIAM Journal on Imaging Sciences 210.1137/18M1228219 Google Scholar Digital Library De Bortoli V Desolneux A Galerne B et al.Image denoising by sparse 3-d transform-domain collaborative filtering IEEE Transactions on Image Processing 22095 2460626 10.1109/TIP.2007.901238 Google Scholar Cross Ref Nonparametric multiscale blind estimation of intensity-frequency-dependent noise IEEE Transactions on Image Processing 23175 3358806 10.1109/TIP.2015.2438537 1408.94111 Google Scholar Digital Library Chen Y He T Image denoising via an adaptive weighted anisotropic diffusion Multidimensional Systems and Signal Processing 2021 32 651 669 10.1007/s11040-x 1458.94024 Google Scholar Digital Library.Chen Y Robust anisotropic diffusion filter via robust spatial gradient estimation Multidimensional Systems and Signal Processing 2021 10.1007/s11048-6 Google Scholar Digital Library.Buades A Coll B Morel JM Non-local means denoising Image Processing On Line 2011 1 208 212 10.5201/_nlm 1259.68220 Google Scholar Cross Ref.Buades A Coll B Morel JM A review of image denoising algorithms, with a new one Multiscale Modeling and Simulation 210.1137/040616024 1108.94004 Google Scholar Cross Ref.The correlation corrected NLM can also be competitive with the state-of-the-art block-matching 3D (BM3D) algorithm and its execution time is much shorter than BM3D. Experimental results show that both quantitative and qualitative performance of the correlation corrected NLM is significantly improved as compared to the other NLM algorithms under large noise. We then propose to add a correlation correction function in the distance calculation to remedy this omission. In this paper, we show that a correlation term previously omitted in theoretical analysis cannot be ignored in patch distance calculation, especially when noise is large. ![]() Therefore, patch distance is paramount to the denoising performance of NLM. Because of these contextually related weights, image structure can be much better preserved for NLM. Patch similarity is measured by the Euclidean distance between two patches and pixels with smaller mutual distance have larger weights. Its distinctive feature is that the weight of a pixel depends on the similarity between two image patches. Non-local means (NLM) remove noise from an image by a weighted average process.
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