Gaussian Patch Mixture Model Guided Low-Rank Covariance Matrix Minimization for Image Denoising*

Image denoising is one of the most important tasks in image processing. In this paper, we study image denoising methods by using similar patches which have low-rank covariance matrices to recover an underlying image which is corrupted by additive Gaussian noise. In order to enhance global patch-matching results, we make use of a Gaussian mixture model with an auxiliary image to determine different groups of patches. The auxiliary image is an output of BM3D. The noisy version of covariance matrix is formed by each group of patches from the given noisy image. Its low-rank version can be estimated by using covariance matrix nuclear norm minimization, and the resulting denoised image can be obtained. Experimental results are reported to show that the proposed method outperforms the state-of-the-art denoising methods, including testing deep learning methods, in the peak signal-to-noise ratio, structural similarity values, and visual quality.