Title :
Performance analysis of support recovery with joint sparsity constraints
Author :
Tang, Gongguo ; Nehorai, Arye
Author_Institution :
Dept. of Electr. & Syst. Eng., Washington Univ. in St. Louis, St. Louis, MO, USA
fDate :
Sept. 30 2009-Oct. 2 2009
Abstract :
In this paper, we analyze the performance of estimating the common support for jointly sparse signals based on their projections onto lower-dimensional space. We formulate support recovery as a multiple-hypothesis testing problem and derive both upper and lower bounds on the probability of error for general measurement matrices, by using Chernoff bound and Fano´s inequality, respectively. When applied to Gaussian measurement ensembles, these bounds give necessary and sufficient conditions to guarantee a vanishing probability of error for majority realizations of the measurement matrix. Our results offer surprising insights into sparse signal reconstruction based on their projections. For example, as far as support recovery is concerned, the well-known bound in compressive sensing is generally not sufficient if the Gaussian ensemble is used. Our study provides an alternative performance measure, one that is natural and important in practice, for signal recovery in com-pressive sensing as well as other application areas taking advantage of signal sparsity.
Keywords :
Gaussian processes; error statistics; matrix algebra; signal processing; Chernoff bound; Fano inequality; Gaussian measurement ensemble; error probability; joint sparsity constraint; multiple-hypothesis testing; signal sparsity; support recovery; Area measurement; Linear matrix inequalities; Performance analysis; Sampling methods; Signal analysis; Signal denoising; Signal reconstruction; Sparse matrices; Sufficient conditions; Testing;
Conference_Titel :
Communication, Control, and Computing, 2009. Allerton 2009. 47th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4244-5870-7
DOI :
10.1109/ALLERTON.2009.5394809