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 socalled “analysis” and “synthesis” approaches as special cases and contains novel hybrid setups. We find corresponding coherencebased recovery guarantees for an 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 Candès et al., ACHA, 2011, for the “analysis” signal recovery problem minimize x Ψ x 1 subject to y − A x 2 ≤ ε by delivering corresponding coherence-based recovery results.
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- ECE Publications