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arXiv · 1205.4551

Sparse Signal Separation in Redundant Dictionaries

Céline Aubel·Christoph Studer·Graeme Pope·Helmut Bölcskei
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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 \leq ε, by delivering corresponding coherence-based recovery results.

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Céline Aubel, Christoph Studer, Graeme Pope, Helmut Bölcskei. 2012-05-21. Sparse Signal Separation in Redundant Dictionaries. https://doi.org/10.1109/isit.2012.6283720

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