Sparse signal separation in redundant dictionaries

Authors

Céline Aubel, Christoph Studer, Graeme Pope, and Helmut Bölcskei

Reference

Proc. of IEEE International Symposium on Information Theory (ISIT), Boston, MA, USA, pp. 2047-2051, July 2012.

Abstract

We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis'' and "synthesis'' approaches as special cases and contains novel hybrid setups. We find corresponding coherence-based recovery guarantees for an l1-norm based separation algorithm. Our results recover those reported in Studer and Baraniuk, ACHA, submitted, for the synthesis setting, provide new recovery guarantees for the analysis setting, and form a basis for comparing performance in the analysis and synthesis settings. As an aside our findings complement the D-RIP recovery results reported in Candès et al., ACHA, 2011, for the "analysis" signal recovery problem: minimize_x ||Ψx||_1 subject to ||y - Ax||_2 ≤ ε, by delivering corresponding coherence-based recovery results.

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