Image completion with alternating direction method of multipliers

Abstract

Image inpainting is useful in many real-life applications. Many existing works on image inpainting base the problem formulation on the low-rank assumption of natural images. Instead of utilizing the rank operator, which is discontinuous and nonconvex, some studies propose to use the nuclear norm as an approximation. However, as we are simultaneously minimizing all the singular values in this approach, the approximation may not be accurate. Besides, apart from being low-rank, most structured and regular images also exhibit sparsity in certain transformed domain. In this report, the results produced by four methods, namely nuclear norm minimization, truncated nuclear norm minimization, nuclear norm minimization with sparsity regularization and truncated nuclear norm minimization with sparsity regularization, are compared in order to evaluate the effectiveness of truncated nuclear norm approximation and sparsity regularization. In addition, the inpainting problem of blurred images is also considered and a centralized sparse representation based algorithm is used to recover the images. Simulations on the ideal image inpainting algorithms show the advantage of truncated nuclear norm approximation and sparsity regularization. Experiments with blurred images also demonstrate some good results.