This paper proposes a detail-preserving image denoising method via cluster-wise progressive PCA (principal component analysis) 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, the 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 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 the state-of-the-art denoising performance in terms of quantitative indices, but also preserves visually important image details best.

Image restoration (IR) is a long-standing challenging problem in low-level image processing. It is of utmost importance to learn good image priors for pursuing visually pleasing results. In this work, we develop a multi-channel and multi-model based denoising autoencoder network as image prior for solving IR problem. Specifically, the network that trained on RGB-channel images is used to construct a prior at first, and then the learned prior is incorporated into single-channel grayscale IR tasks. To achieve the goal, we employ the auxiliary variable technique to integrate the higher-dimensional network-driven prior information into the iterative restoration procedure. Additionally, according to the weighted aggregation idea, a multi-model strategy is put forward to enhance the network stability that favors to avoid getting trapped in local optima. Extensive experiments on image deblurring and deblocking tasks show that the proposed algorithm is efficient, robust and yields state-of-the-art restoration quality on grayscale images.