Sparse signal separation in redundant dictionaries
AuthorsCéline Aubel, Christoph Studer, Graeme Pope, and Helmut Bölcskei
ReferenceProc. of IEEE International Symposium on Information Theory (ISIT), Boston, MA, USA, pp. 2047 - 2051, July 2012.
AbstractWe 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.
Download this document:
Copyright Notice: © 2012 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.