Sparsity and the Bayesian Perspective

Understand

Sparsity has been recently introduced in cosmology for weak-lensing and 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, based on arguments derived from a Bayesian perspective.
• Trying 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.