An IHT algorithm for sparse recovery from subexponential measurements

Simon Foucart () and Guillaume Lecué ()
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Simon Foucart: Texas A&M University
Guillaume Lecué: CREST; ENSAE; CNRS

No 2017-31, Working Papers from Center for Research in Economics and Statistics

Abstract: A matrix whose entries are independent subexponential random variables is not likely to satisfy the classical restricted isometry property in the optimal regime of parameters. However, it is known that uniform sparse recovery is still possible with high probability in the optimal regime if ones uses l1-minimization as a recovery algorithm. We show in this note that such a statement remains valid if one uses a new variation of iterative hard thresholding as a recovery algorithm. The argument is based on a modified restricted isometry property featuring the l1-norm as the inner norm. ;Classification-JEL: 65F10; 15A29; 94A12

Keywords: compressive sensing; sparse recovery; iterative hard thresholding; restricted isometry property; subexponential random variable (search for similar items in EconPapers)
Pages: 7 pages
Date: 2017-01-01
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