Sparse Signal Recovery via l1 Minimization

The purpose of this paper is to give a brief overview of the main results for sparse recovery via L optimization. Given a set of K linear measurements y=Ax where A is a Ktimes;N matrix, the recovery is performed by solving the convex program minparxpar 1 subject to Ax=y, where parxpar 1 :=Sigma t=0...

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Bibliographic Details
Published in2006 40th Annual Conference on Imformation [sic.] Sciences and Systems : Princeton, N.J., March 22-24, 2006 pp. 213 - 215
Main Author Romberg, J.K.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.03.2006
Subjects
Energy measurement
Equations
Linear algebra
Mathematics
Measurement errors
Noise measurement
Performance evaluation
Size measurement
Sparse matrices
Uncertainty
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ISBN9781424403493
1424403499
DOI10.1109/CISS.2006.286464

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Summary:The purpose of this paper is to give a brief overview of the main results for sparse recovery via L optimization. Given a set of K linear measurements y=Ax where A is a Ktimes;N matrix, the recovery is performed by solving the convex program minparxpar 1 subject to Ax=y, where parxpar 1 :=Sigma t=0 N-1 |x(t)|. If x is S-sparse (it contains only S nonzero components), and the matrix A obeys a certain type of uncertainty principle then the above equation will recover x exactly when K is on the order of S log N. The number of measurements it takes to acquire a sparse signal is within a constant log factor of its inherent complexity, even though we have no idea which components are important before hand. The recovery procedure can be made stable against measurement errors, and is computationally tractable.
ISBN:9781424403493
1424403499
DOI:10.1109/CISS.2006.286464