Entropy and astronomical data analysis: Perspectives from multiresolution analysis

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.