Bayesian Framework with Non-local and Low-rank Constraint for Image Reconstruction

Built upon the similar methodology of `grouping and collaboratively filtering', the proposed algorithm recovers image patches from the array of similar noisy patches based on the assumption that their noise-free versions or approximation lie in a low dimensional subspace and has a low rank. Based on the analysis of the effect of noise and perturbation on the singular value, a weighted nuclear norm is defined to replace the conventional nuclear norm. Corresponding low-rank decomposition model and singular value shrinkage operator are derived. Taking into account the difference between the distribution of the signal and the noise, the weight depends not only on the standard deviation of noise, but also on the rank of the noise-free matrix and the singular value itself. Experimental results in image reconstruction tasks show that at relatively low computational cost the performance of proposed method is very close to state-of-the-art reconstruction methods BM3D and LSSC even outperforms them in restoring and preserving structure.