Sparsity and the Bayesian Perspective

Jean-Luc Starck (1) , David Donoho (2) , Jalal M. Fadili (3) , Anais Rassat (4)

1 AIM (UMR7158 / UMR_E_9005 / UM_112) - Astrophysique Interprétation Modélisation
2 Department of Statistics [Stanford]
3 Equipe Image - Laboratoire GREYC - UMR6072
4 LASTRO - Laboratoire d'Astrophysique [Versoix]

Sparsity 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.

Mots clés: statistical methods; cosmic background radiation; data analysis

Domaines: Traitement des images [eess.IV]

Jean-Luc Starck, David Donoho, Jalal M. Fadili, Anais Rassat. Sparsity and the Bayesian Perspective. Astronomy and Astrophysics - A&A, 2013, 552, A133, 5 pp. ⟨10.1051/0004-6361/201321257⟩. ⟨hal-00927047⟩