Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 9, Pages 4595-4607Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2051150
Keywords
Compressive sensing; modified-CS; partially known support; prior knowledge; sparse reconstruction
Categories
Funding
- NSF [ECCS-0725849, CCF-0917015]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0917015] Funding Source: National Science Foundation
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We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The known part of the support, denoted, may be available from prior knowledge. Alternatively, in a problem of recursively reconstructing time sequences of sparse spatial signals, one may use the support estimate from the previous time instant as the known part. The idea of our proposed solution (modified-CS) is to solve a convex relaxation of the following problem: find the signal that satisfies the data constraint and is sparsest outside of. We obtain sufficient conditions for exact reconstruction using modified-CS. These are much weaker than those needed for compressive sensing (CS) when the sizes of the unknown part of the support and of errors in the known part are small compared to the support size. An important extension called regularized modified-CS (RegModCS) is developed which also uses prior signal estimate knowledge. Simulation comparisons for both sparse and compressible signals are shown.
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