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 decomposition method called MCA (morphological component analysis), designed for the separation of linearly combined texture and cartoon layers in a given image (see [J.-L. Starck, M. Elad, D.L. Donoho, Image decomposition via the combination of sparse representations and a variational approach, IEEE Trans. Image Process. (2004), in press] and [J.-L. Starck, M. Elad, D.L. Donoho, Redundant multiscale transforms and their application for morphological component analysis, Adv. Imag. Electron Phys. ( 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.

Abstract. The Maximum Entropy Method is well-known and widely used in image analysis in astronomy. In its standard form it presents certain drawbacks, such an underestimation of the photometry. Various refinements of MEM have been proposed over the years. We review in this paper the main entropy functionals which have been proposed and discuss each of them. We define, from a conceptual point of view, what a good definition of entropy should be in the framework of astronomical data processing. We show how a definition of multiscale entropy fulfills these requirements. We show how multiscale entropy can be used for many applications, such as signal or image filtering, multi-channel data filtering, deconvolution, background fluctuation analysis, and astronomical image content analysis.