Sparsity and morphological diversity for multivalued data analysis

Jérome Bobin (1) , Yassir Moudden (2) , Jean-Luc Starck (2) , Jalal M. Fadili (3)

1 ACM - Department of Applied & Computational Mathematics
2 DAPNIA - Département d'Astrophysique, de physique des Particules, de physique Nucléaire et de l'Instrumentation Associée
3 Equipe Image - Laboratoire GREYC - UMR6072

The recent development of multi-channel sensors has motivated interest in devising new methods for the coherent processing of multivariate data. An extensive work has already been dedicated to multivariate data processing ranging from blind source separation (BSS) to multi/hyper-spectral data restoration. Previous work1 has emphasized on the fundamental role played by sparsity and morphological diversity to enhance multichannel signal processing. GMCA is a recent algorithm for multichannel data analysis which was used successfully in a variety of applications including multichannel sparse decomposition, blind source separation (BSS), color image restoration and inpainting. Inspired by GMCA, a recently introduced algorithm coined HypGMCA is described for BSS applications in hyperspectral data processing. It assumes the collected data is a linear instantaneous mixture of components exhibiting sparse spectral signatures as well as sparse spatial morphologies, each in specified dictionaries of spectral and spatial waveforms. We report on numerical experiments with synthetic data and application to real observations which demonstrate the validity of the proposed method.

Domaines: Traitement des images [eess.IV]

Jérome Bobin, Yassir Moudden, Jean-Luc Starck, Jalal M. Fadili. Sparsity and morphological diversity for multivalued data analysis. SPIE Wavelets XIII, Aug 2009, San Diego, United States. pp.7446-48. ⟨hal-00813862⟩