This paper describes a novel inpainting algorithm that is capable of filling in holes in overlapping texture and cartoon image layers. This algorithm is a direct extension of a recently developed sparse-representation-based image (2004) 132]). In this extension, missing pixels fit naturally into the separation framework, producing separate layers as a by-product of the inpainting process. As opposed to the inpainting system proposed by Bertalmio et al., where image decomposition and filling-in stages were separated as two blocks in an overall system, the new approach considers separation, hole-filling, and denoising as one unified task. We demonstrate the performance of the new approach via several examples.  2005 Elsevier Inc. All rights reserved.
On the other hand, their approach REF considers these as one unified task.
Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)
Applied and Computational Harmonic Analysis
Mathematics