Rank minimization approach to image inpainting using null space based alternating optimization

This paper proposes a novel image inpainting based on the matrix rank minimization. Assuming that an image can be modeled by the autoregressive (AR) model, this paper formulates the image inpainting problem as the signal recovery problem of an AR model. The main result of this paper is to reformulate this problem as the matrix rank minimization and to provide an inpainting algorithm based on the null space based alternating optimization (NSAO) algorithm. Numerical examples show that the proposed algorithm recovers missing pixels efficiently.