3 research outputs found
Sparse Signal Separation in Redundant Dictionaries
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 Cand\`es et al., ACHA, 2011, for the "analysis" signal recovery
problem: minimize_x ||{\Psi}x||_1 subject to ||y - Ax||_2 \leq {\epsilon}, by
delivering corresponding coherence-based recovery results.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT),
Boston, MA, July 201