Detail-Preserving Image Denoising via Adaptive Clustering and Progressive PCA Thresholding

This paper proposes a detail-preserving image denoising method via cluster-wise progressive principal component analysis (PCA) thresholding based on the Marchenko-Pastur (MP) law in random matrix theory. According to random matrix theory, an efficient and stable noise-level estimation method is also presented. Specifically, a global Gaussian noise level is estimated by interpreting the relationship between noise and eigenvalues of PCA for noisy patch matrices via the MP law in conjunction with the observation that vectors extracted from a noise-free image often lie in a low-dimensional subspace. Before noise removal, an adaptive clustering method is developed to automatically determine a suitable number of clusters segregating patches with different features (edges and textures). To denoise each cluster matrix, progressive PCA thresholding is performed. First, a hard thresholding of singular values in the singular value decomposition domain based on the MP law is applied to find a low-rank approximation to the cluster matrix. Second, the remaining noises of the low-rank matrix are further removed in the PCA transform domain using a special soft thresholding, i.e., the linear minimum mean-square-error technique with locally estimated parameters. The experiments show that the proposed method not only achieves state-of-the-art denoising performance in terms of quantitative indices, but also preserves visually important image details best.