Low-rank Image Denoising Based on Minimum Variance Estimator

Natural images always exhibit a certain nonlocal self-similarity property, which implies that the patch matrix formed by similar image patches is low-rank. Based on the low-rank approximation and the minimum variance estimate theory, this paper proposes an efficient iterative denoising method. The proposed method translates the image denoising issue into the estimate of some low-rank matrices by constructing similar patch matrices. The minimum variance estimator is exploited to yield the estimates of these matrices, and a denoised image is achieved by aggregating all denoised image patches. In order to further reduce the residual noise in the denoised image, an iterative version of the proposed method based on back-projection process is introduced. Experimental results show that the proposed method obtains not only higher peak signal-to-noise ratio and feature structural similarity values but also better visual quality.