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Sparse Vector Distributions and Recovery from Compressed Sensing

By Bob L. Sturm

Abstract

It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two morals of this work are: 1) any judgement of the recovery performance of one algorithm over that of another must be prefaced by the conditions for which this is observed to be true, including sparse vector distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal.Comment: Originally submitted to IEEE Signal Processing Letters in March 2011, but rejected June 2011. Revised, expanded, and submitted July 2011 to EURASIP Journal special issue on sparse signal processin

Topics: Computer Science - Data Structures and Algorithms, F.2.1, G.1.2, G.1.3, G.1.6
Year: 2011
OAI identifier: oai:arXiv.org:1103.6246
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