Distortion-based achievability conditions for joint estimation of sparse signals and measurement parameters from undersampled acquisitions

Mehmet Akcakaya, Vahid Tarokh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we consider an undersampling system model of the form y = A(T(x, θ)) + n, where x is a k-sparse signal, T(·, · is a (possibly non-linear) function specified by a parameter vector θ and acting on x, A is a sensing matrix, and n is additive measurement noise. We consider an information theoretic decoder that aims to recover the sparse signal and the transformation parameter vector jointly, and study the achievability conditions for estimating the underlying signal within a specified ℓ2 distortion for Gaussian sensing matrices. We compare the achievable distortion of the joint estimation process to that of the standard noisy compressed sensing model, where the sparse signal is directly measured with a sensing matrix with the same number of measurements. We also provide a numerical example to illustrate potential applications.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages291-295
Number of pages5
DOIs
StatePublished - Dec 19 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
CountryTurkey
CityIstanbul
Period7/7/137/12/13

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