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Sparsity and the Bayesian Perspective

By Jean-Luc Starck, David Donoho, Jalal M. Fadili and Anais Rassat

Abstract

International audienceSparsity has recently been introduced in cosmology for weak-lensing and cosmic microwave background (CMB) data analysis for different applications such as denoising, component separation, or inpainting (i.e., filling the missing data or the mask). Although it gives very nice numerical results, CMB sparse inpainting has been severely criticized by top researchers in cosmology using arguments derived from a Bayesian perspective. In an attempt to understand their point of view, we realize that interpreting a regularization penalty term as a prior in a Bayesian framework can lead to erroneous conclusions. This paper is by no means against the Bayesian approach, which has proven to be very useful for many applications, but warns against a Bayesian-only interpretation in data analysis, which can be misleading in some cases

Topics: data analysis, statistical methods, cosmic background radiation, [ INFO.INFO-TI ] Computer Science [cs]/Image Processing
Publisher: EDP Sciences
Year: 2013
DOI identifier: 10.1051/0004-6361
OAI identifier: oai:HAL:hal-00927047v1
Provided by: Hal-Diderot

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