Cosparse Analysis Modeling

Sangnam Nam (1) , Mike E. Davies (2) , Michael Elad (3) , Rémi Gribonval (1)

1 METISS - Speech and sound data modeling and processing
2 Institute for Digital Communication Joint Research Institute for Signal & Image Processing School of Engineering and Electronics - University of Edinburgh
3 Department of Computer Science [Haifa]

In the past decade there has been a great interest in a synthesis-based model for signals, based on sparse and redundant representations. This work considers an alternative analysis-based model, where an analysis operator multiplies the signal, leading to a cosparse outcome. We consider this analysis model, in the context of a generic missing data problem. Our work proposes a uniqueness result for the solution of this problem, based on properties of the analysis operator and the measurement matrix. A new greedy algorithm for solving the missing data problem is proposed along with theoretical study of the success of the algorithm and experimental results.

Mots clés: sparse representation; inverse problems; algorithms; cosparse analysis model

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

Sangnam Nam, Mike E. Davies, Michael Elad, Rémi Gribonval. Cosparse Analysis Modeling. Workshop on Signal Processing with Adaptive Sparse Structured Representations, Jun 2011, Edinburgh, United Kingdom. ⟨inria-00587943⟩