Missing region recovery by promoting blockwise low-rankness

In this paper, we propose a novel missing region recovery method by promoting blockwise low-rankness. It is natural to assume that images often have local repetitive structures. Hence, any small block extracted from an image is expected to be a low-rank matrix. Based on this assumption, we formulate missing region recovery as a convex optimization problem via newly introduced block nuclear norm which promotes blockwise low-rankness of an image with missing regions. An iterative scheme for approximating a global minimizer of the problem is also presented. The scheme is based on the alternating direction method of multipliers (ADMM) and allows us to restore missing regions efficiently. Experimental results reveal that the proposed method can recover missing regions with detailed local structures.