EM algorithm for sparse representation-based image inpainting

We introduce an expectation-maximization (EM) algorithm for image inpainting based on a penalized likelihood formulated using linear sparse representations. Taking advantage of the sparsity of representations, a regularization through a prior penalty is imposed on the reconstructed coefficients. From a statistical point of view, the inpainting can be viewed as an estimation problem with missing data. The EM framework is a general iterative algorithm for ML estimation in such situations. The EM framework gives a principled way to establish formally the idea that missing samples can be recovered based on sparse representations. Furthermore, owing to its well known theoretical properties, the EM algorithm allows to investigate the convergence behavior of the inpainting algorithm.