Image inpainting by block-based linear regression with optimal block selection

Estimation of missing entries in a multivariate data is one of classical problems in the field of statistical science. One of most popular approaches for this problem is linear regression based on the EM algorithm. When we consider to apply this approach to block-based image inpainting problems, we have additional information, that is, a target lost pixel could be included in multiple blocks, which implies that we have multiple candidates of estimates for the pixel. In such cases, we have to choose a good estimate among the multiple candidates. In this paper, we propose a novel image inpainting method incorporating optimal block selection in terms of the expected squared errors among multiple candidates of the estimate for the target pixel. Results of numerical examples are also shown to verify the efficacy of the proposed method.