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Cite Details

Rick Chartrand, "Exact reconstructions of sparse signals via nonconvex minimization", IEEE Signal Process. Lett., vol. 14, pp. 707--710, 2007


Several authors have shown recently that is possible to reconstruct exactly a sparse signal from fewer linear measurements than would be expected from traditional sampling theory. The methods used involve computing the signal of minimum 1 norm among those having the given measurements. We show that by replacing the 1 norm with the p norm with p<1, exact reconstruction is possible with substantially fewer measurements. We give a theorem in this direction, and many numerical examples, both in one complex dimension, and larger-scale examples in two real dimensions.

BibTeX Entry

author = {Rick Chartrand},
title = {Exact reconstructions of sparse signals via nonconvex minimization},
year = {2007},
urlpdf = {http://math.lanl.gov/Research/Publications/Docs/chartrand-2007-exact.pdf},
journal = {IEEE Signal Process. Lett.},
volume = {14},
pages = {707--710}