Kronecker component with robust low-rank dictionary for image denoising

Robust Kronecker Component Analysis (RKCA) model is a newly proposed denoising method, which transforms the basic sparse representation model used for 2-D data into the tensor sparse representation used for 3-D data. This model is based on the idea that the dictionary in the basic sparse representation model can be separated into two separable dictionaries using the Kronecker Product and the mode-n product. Moreover, the original 3-D data can also be decomposed into a sparse matrix and two dictionaries by using Tucker factorization. It uses the Frobenius norm constraint to get two low-rank dictionaries. In this paper, we take the Nuclear norm into RKCA to better capture the low-rank property of the two dictionaries. Firstly, we design a novel denoising model named Kronecker Component with Low-Rank Dictionary (KCLD), which replaces the Frobenius norm by Nuclear norm in order to capture the low-rank property better. Further, we design a more effective denoising model named Kronecker Component with Robust Low-Rank Dictionary (KCRD) by combining the Frobenius norm and the Nuclear norm. KCRD fuses the advantages of Frobenius norm and the Nuclear norm, thus can get the better low-rank dictionary. Then, an augmented Lagrange multiplier method is used by convex relaxation of the split variable to optimize the two proposed model. Last, through the comparison of a large number of experiments, our models are more competitive and effective than other proposed denoising methods in different types of images.