Reweighted Low-Rank Factorization With Deep Prior for Image Restoration

The low-rank recovery is a powerful tool to restore images from incomplete and corrupted observations. Conventional low-rank recovery techniques employ the reweighted nuclear norm minimization, which requires performing the full singular value decomposition and thus is computationally expensive. Using the scheme of bilinear factorization, we propose the Reweighted Low-rank Matrix Factorization (RLMF) method for single channel image restoration. The RLMF method can not only inherit the computational efficiency of bilinear factorization, but also incorporate the empirical distribution of the singular values in natural images. Then, considering the correlation between image channels, we generalize the reweighted nuclear norm from matrices to tensors, and develop the Reweighted Low-rank Tensor Factorization (RLTF) method for multichannel image restoration. Moreover, we enhance the RLMF and RLTF methods by introducing the deep image prior information, which is capable of capturing the implicit image structure through the neural network architecture to improve restoration accuracy. Experimental results show the computational efficiency of the proposed low-rank factorization scheme, and the superior restoration accuracy of the proposed methods compared with the state-of-the-art methods.