Signal, Image and Video Processing

, Volume 3, Issue 3, pp 251–264

Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients

Original Paper

DOI: 10.1007/s11760-008-0076-1

Cite this article as:
Kowalski, M. & Torrésani, B. SIViP (2009) 3: 251. doi:10.1007/s11760-008-0076-1


Sparse regression often uses ℓp norm priors (with p < 2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of the ℓ1,2 and ℓ2,1 norms leads to new group shrinkage operators. Mixed norm priors are shown to be particularly efficient in a generalized basis pursuit denoising approach, and are also used in a context of morphological component analysis. A suitable version of the Block Coordinate Relaxation algorithm is derived for the latter. The group-shrinkage operators are then modified to overcome some limitations of the mixed-norms. The proposed group shrinkage operators are tested on simulated signals in specific situations, to illustrate and compare their different behaviors. Results on real data are also used to illustrate the relevance of the approach.


Mixed-norms Time–frequency decompositions Sparse representations 

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.LATP, CMIMarseille Cedex 13France

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