TY - JOUR
T1 - Ranked sparse signal support detection
AU - Fletcher, Alyson K.
AU - Rangan, Sundeep
AU - Goyal, Vivek K.
N1 - Funding Information:
Manuscript received November 02, 2011; revised April 24, 2012; accepted June 18, 2012. Date of publication July 16, 2012; date of current version October 09, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Namrata Vaswani. The work of V. K Goyal was supported in part by the National Science Foundation under CAREER Grant No. 0643836. This work was presented in part at the IEEE International Symposium on Information Theory, Seoul, Korea, June–July 2009 A. K. Fletcher is with the Department of Electrical Engineering, University of California, Santa Cruz, CA 95064 USA (e-mail: [email protected]).
PY - 2012
Y1 - 2012
N2 - This paper considers the problem of detecting the support (sparsity pattern) of a sparse vector from random noisy measurements. Conditional power of a component of the sparse vector is defined as the energy conditioned on the component being nonzero. Analysis of a simplified version of orthogonal matching pursuit (OMP) called sequential OMP (SequOMP) demonstrates the importance of knowledge of the rankings of conditional powers. When the simple SequOMP algorithm is applied to components in nonincreasing order of conditional power, the detrimental effect of dynamic range on thresholding performance is eliminated. Furthermore, under the most favorable conditional powers, the performance of SequOMP approaches maximum likelihood performance at high signal-to-noise ratio.
AB - This paper considers the problem of detecting the support (sparsity pattern) of a sparse vector from random noisy measurements. Conditional power of a component of the sparse vector is defined as the energy conditioned on the component being nonzero. Analysis of a simplified version of orthogonal matching pursuit (OMP) called sequential OMP (SequOMP) demonstrates the importance of knowledge of the rankings of conditional powers. When the simple SequOMP algorithm is applied to components in nonincreasing order of conditional power, the detrimental effect of dynamic range on thresholding performance is eliminated. Furthermore, under the most favorable conditional powers, the performance of SequOMP approaches maximum likelihood performance at high signal-to-noise ratio.
KW - Compressed sensing
KW - convex optimization
KW - lasso
KW - maximum likelihood estimation
KW - orthogonal matching pursuit
KW - random matrices
KW - sparse Bayesian learning
KW - sparsity
KW - thresholding
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U2 - 10.1109/TSP.2012.2208957
DO - 10.1109/TSP.2012.2208957
M3 - Article
AN - SCOPUS:84867498193
SN - 1053-587X
VL - 60
SP - 5919
EP - 5931
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 11
M1 - 6241445
ER -