Image Completion with the Regularization Constraint

Abstract

Image inpainting is a process of restoring missing parts of an image, which is widely be used in many real-life applications. One of the approaches on image inpainting is to use the low-rank assumption. However, it is found that the matrix rank is a discontinuous and non-convex function. Because of these, some studies proposed applying nuclear norm as a convex surrogate of the rank operator. Besides, a regularization term is added into the objective function since natural images have both low-rank and sparse features in the transformed domain. In this project, two image inpainting algorithms were studied, namely nuclear norm minimization and nuclear norm minimization with sparsity regularization. The performances of these two algorithms were also evaluated. In addition, some examples on image inpainting applications are demonstrated in this project. The simulation results showed that sparsity regularization can improve the inpainting quality. Also, it was found that the weighting parameter of the regularization term should be moderate, which cannot be too small or too large.