Morphological Diversity and Sparsity for Multichannel Data Restoration

Jérome Bobin (1) , Yassir Moudden (1) , Jalal M. Fadili (2) , Jean-Luc Starck (1)

1 DAPNIA - Département d'Astrophysique, de physique des Particules, de physique Nucléaire et de l'Instrumentation Associée
2 Equipe Image - Laboratoire GREYC - UMR6072

Over the last decade, overcomplete dictionaries and the very sparse signal representations they make possible, have raised an intense interest from signal processing theory. In a wide range of signal processing problems, sparsity has been a crucial property leading to high performance. As multichannel data are of growing interest, it seems essential to devise sparsity-based tools accounting for such specific multichannel data. Sparsity has proved its efficiency in a wide range of inverse problems. Hereafter, we address some multichannel inverse problems issues such as multichannel morphological component separation and inpainting from the perspective of sparse representation. In this paper, we introduce a new sparsity-based multichannel analysis tool coined multichannel Morphological Component Analysis (mMCA). This new framework focuses on multichannel morphological diversity to better represent multichannel data. This paper presents conditions under which the mMCA converges and recovers the sparse multichannel representation. Several experiments are presented to demonstrate the applicability of our approach on a set of multichannel inverse problems such as morphological component decomposition and inpainting.

Mots clés: Sparsity; Overcomplete representations; Multichannel data; Restoration

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

Jérome Bobin, Yassir Moudden, Jalal M. Fadili, Jean-Luc Starck. Morphological Diversity and Sparsity for Multichannel Data Restoration. Journal of Mathematical Imaging and Vision, 2009, 33 (2), pp.149-168. ⟨10.1007/s10851-008-0065-6⟩. ⟨hal-00813969⟩