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We formulate a unified framework for the separation of signals that are sparse in &#x201C;morphologically&#x201D; different redundant dictionaries. This formulation incorporates the so-called &#x201C;analysis&#x201D; and &#x201C;synthesis&#x201D; approaches as special cases and contains novel hybrid setups. We find corresponding coherence-based recovery guarantees for an &#x2113;1-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 Cande&#x0300;s et al., ACHA, 2011, for the &#x201C;analysis&#x201D; signal recovery problem minimize x ||&#x03A8;x&#x0303;||1 subject to ||y - Ax&#x0303;||2 &#x2264; &#x03F5; by delivering corresponding coherence-based recovery results.

Sparse signal separation in redundant dictionaries