TY - GEN
T1 - Support recovery in compressed sensing
T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009
AU - Karbasi, Amin
AU - Hormati, Ali
AU - Mohajer, Soheil
AU - Vetterli, Martin
PY - 2009
Y1 - 2009
N2 - Compressed sensing (CS) deals with the reconstruction of sparse signals from a small number of linear measurements. One of the main challenges in CS is to find the support of a sparse signal from a set of noisy observations. In the CS literature, several information-theoretic bounds on the scaling law of the required number of measurements for exact support recovery have been derived, where the focus is mainly on random measurement matrices. In this paper, we investigate the support recovery problem from an estimation theory point of view, where no specific assumption is made on the underlying measurement matrix. By using the Hammersley-Chapman-Robbins (HCR) bound, we derive a fundamental lower bound on the performance of any unbiased estimator which provides necessary conditions for reliable ℓ2-norm support recovery. We then analyze the optimal decoder to provide conditions under which the HCR bound is achievable. This leads to a set of sufficient conditions for reliable ℓ2-norm support recovery.
AB - Compressed sensing (CS) deals with the reconstruction of sparse signals from a small number of linear measurements. One of the main challenges in CS is to find the support of a sparse signal from a set of noisy observations. In the CS literature, several information-theoretic bounds on the scaling law of the required number of measurements for exact support recovery have been derived, where the focus is mainly on random measurement matrices. In this paper, we investigate the support recovery problem from an estimation theory point of view, where no specific assumption is made on the underlying measurement matrix. By using the Hammersley-Chapman-Robbins (HCR) bound, we derive a fundamental lower bound on the performance of any unbiased estimator which provides necessary conditions for reliable ℓ2-norm support recovery. We then analyze the optimal decoder to provide conditions under which the HCR bound is achievable. This leads to a set of sufficient conditions for reliable ℓ2-norm support recovery.
UR - http://www.scopus.com/inward/record.url?scp=70449516036&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2009.5206485
DO - 10.1109/ISIT.2009.5206485
M3 - Conference contribution
AN - SCOPUS:70449516036
SN - 9781424443130
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 679
EP - 683
BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009
Y2 - 28 June 2009 through 3 July 2009
ER -