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In recent years, sparse representation theory and low-rank approximation model have been widely used in signal and image processing fields. In the study of natural image denoising, non-local similarity method can enhance the correlation of grouped image blocks, and a low rank prior is used to devise a bilateral sparse representation of the image matrix, consequently achieving the purpose of removing additive white Gaussian noise. However, problems such as how to select thresholds after a singular value shrinkage, and how to eliminate image artifacts in removing noise especially with high levels, have not been resolved. In this paper, a low rank adaptive singular value thresholding (ASVT) denoising algorithm based on singular value decomposition(SVD) is proposed. Our method uses random matrix and asymptotic matrix reconstruction theory to scientifically select the threshold of singular value thresholding. At the same time, a dual-domain filtering method is used to process the visual artifacts after image denoising by ASVT, which we call collaborative singular value thresholding (CSVT) algorithm. The experimental results show that the proposed algorithm has a certain improvement in subjective visual effects, and objective quantitative indicators compared with some related advanced denoising algorithms.

An Efficient Collaborative Filtering Method for Image Noise and Artifact Removal