An overview of inverse problem regularization using sparsity

Jean-Luc Starck (1) , Jalal M. Fadili (2)

1 AIM (UMR7158 / UMR_E_9005 / UM_112) - Astrophysique Interprétation Modélisation
2 Equipe Image - Laboratoire GREYC - UMR6072

Sparsity constraints are now very popular to regularize inverse problems. We review several approaches which have been proposed in the last ten years to solve inverse problems such as inpainting, deconvolution or blind source separation. We will focus especially on optimization methods based on iterative thresholding methods to derive the solution.

Mots clés: Sparsity; Deconvolution; Blind Source Separation; inpainting; Compressed Sensing; iterative thresholding

Domaines: Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Jean-Luc Starck, Jalal M. Fadili. An overview of inverse problem regularization using sparsity. IEEE ICIP 2009 - 16th IEEE International Conference on Image Processing, Nov 2009, Le Caire, Egypt. pp.1453 - 1456, ⟨10.1109/ICIP.2009.5414556⟩. ⟨hal-00813693⟩