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Title: "Analysis prior with redundant dictionaries for Compressed Sensing"

Speaker: Kevin Degraux

Location: "Shannon" Seminar Room, Place du Levant 3, Maxwell Building, 1st floor

Date / Time (duration): Wednesday 17/12/2014, 10h00 (~ 45')



This presentation is mainly based on the paper: E. J. Candès, Y. C. Eldar, D. Needell, and P. Randall, “Compressed sensing with coherent and redundant dictionaries,” Appl. Comput. Harmon. Anal., vol. 31, no. 1, pp. 59–73, Jul. 2011. arXiv:1005.2613

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is viable in this context, but also that accurate recovery is possible via an {$\ell_1$}-analysis optimization problem. We introduce a condition on the measurement/sensing matrix, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries. This condition imposes no incoherence restriction on the dictionary and our results may be the first of this kind. We discuss practical examples and the implications of our results on those applications, and complement our study by demonstrating the potential of {$\ell_1$}-analysis for such problems.

The talk will mainly follow the structure of the paper and present additional comments and insights, notably from the work of Nam et al. about the cosparse analysis.


Last updated December 02, 2016, at 02:45 PM