Sparse signal separation in redundant dictionaries


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


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

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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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