An Image Denoising Model via the Reconciliation of the Sparsity and Low-Rankness of the Dictionary Domain Coefficients

Abstract

Sparse coding has achieved great success in various image restoration tasks. However, if the sparse representation coefficients of the structure (low-frequency information) and texture (high-frequency information) components of the image are under the same penalty constraint, the restoration effect may not be ideal. In this paper, an image denoising model combining mixed norm and weighted nuclear norm as regularization terms is proposed. The proposed model simultaneously exploits the group sparsity of the high frequency and low-rankness of the low frequency in dictionary-domain. The mixed norm is used to constrain the high frequency part and the weighted nuclear norm is used to constrain the low frequency part. In order to make the proposed model easy to solve under the framework of alternative direction multiplier method (ADMM), iterative shrinkage threshold method and weighted nuclear norm minimization method are used to solve the two sub-problems. The validity of the model is verified experimentally through comparison with some state-of-the-art methods.