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Sparse Vector Distributions and Recovery from Compressed Sensing
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
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