DocumentCode :
3250473
Title :
Sparse signal recovery under Poisson statistics
Author :
Motamedvaziri, Delaram ; Rohban, Mohammad Hossein ; Saligrama, Venkatesh
Author_Institution :
ECE Dept., Boston Univ., Boston, MA, USA
fYear :
2013
fDate :
2-4 Oct. 2013
Firstpage :
1450
Lastpage :
1457
Abstract :
We are motivated by problems that arise in a number of applications such as explosives detection and online Marketing, where the observations are governed by Poisson statistics. Here each observation is a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many conventional problems observations here are not identically distributed since they are associated with different sensing modalities. We analyse the performance of a Maximum Likelihood (ML) decoder, which for our Poisson setting is computationally tractable. We derive fundamental sample complexity bounds for sparse recovery in the high-dimensional setting. We show that when the sensing matrix satisfies the so-called Restricted Eigenvalue (RE) condition the ℓ1 regularized ML decoder is consistent. Moreover, it converges exponentially fast in terms of number of observations. Our results apply to both deterministic and random sensing matrices and we present several results for both cases.
Keywords :
compressed sensing; eigenvalues and eigenfunctions; maximum likelihood decoding; sparse matrices; stochastic processes; ML decoder; Poisson random variable; Poisson statistics; explosives detection; high-dimensional Poisson setting; maximum likelihood decoder; online marketing; restricted eigenvalue condition; sensing matrix; sparse linear superposition; sparse signal recovery; Robustness; Poisson Model Selection; Regularized Maximum Likelihood; Sparse Recovery;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Communication, Control, and Computing (Allerton), 2013 51st Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4799-3409-6
Type :
conf
DOI :
10.1109/Allerton.2013.6736698
Filename :
6736698
Link To Document :
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