Entropy and astronomical data analysis: Perspectives from multiresolution analysis

¹ DAPNIA/SEI-SAP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
² Statistics Department, Stanford University, Sequoia Hall, Stanford, CA 94305 USA
³ School of Computer Science, The Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland
⁴ CDS, Observatoire Astronomique de Strasbourg, 11 rue de l'Université, 67000 Strasbourg, France

Corresponding author: J.-L. Starck, jstarck@cea.fr

Received: 30 October 2000
Accepted: 27 December 2000

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.