Communications-inspired projection design with application to compressive sensing
Abstract
We consider the recovery of an underlying signal x ∈ ℂm based on projection measurements
of the form y = Mx+w, where y ∈ ℂℓ and w is measurement noise; we are interested in
the case ℓ ≪ m. It is assumed that the signal model p(x) is known and that w ~ CN(w;
0,Σw) for known Σ w. The objective is to design a projection matrix M ∈ ℂℓ×m to maximize
key information-theoretic quantities with operational significance, including the
mutual information between the signal and the projections I(x; y) or the Rényi entropy
of the projections hα (y) (Shannon entropy is a special case). By capitalizing on
explicit characterizations of the gradients of the information measures with respect
to the projection matrix, where we also partially extend the well-known results of
Palomar and Verdu ́ from the mutual information to the Rényi entropy domain, we reveal
the key operations carried out by the optimal projection designs: mode exposure and
mode alignment. Experiments are considered for the case of compressive sensing (CS)
applied to imagery. In this context, we provide a demonstration of the performance
improvement possible through the application of the novel projection designs in relation
to conventional ones, as well as justification for a fast online projection design
method with which state-of-the-art adaptive CS signal recovery is achieved. © 2012
Society for Industrial and Applied Mathematics.
Type
Journal articlePermalink
https://hdl.handle.net/10161/8952Published Version (Please cite this version)
10.1137/120878380Publication Info
Carson, WR; Chen, M; Rodrigues, MRD; Calderbank, R; & Carin, L (2012). Communications-inspired projection design with application to compressive sensing.
SIAM Journal on Imaging Sciences, 5(4). pp. 1182-1212. 10.1137/120878380. Retrieved from https://hdl.handle.net/10161/8952.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Robert Calderbank
Charles S. Sydnor Distinguished Professor of Computer Science
Robert Calderbank is Director of the Information Initiative at Duke University, where
he is Professor of Electrical Engineering, Computer Science and Mathematics. He joined
Duke in 2010, completed a 3 year term as Dean of Natural Sciences in August 2013,
and also served as Interim Director of the Duke Initiative in Innovation and Entrepreneurship
in 2012. Before joining Duke he was Professor of Electrical Engineering and Mathematics
at Princeton University where he also directed the Program i
Lawrence Carin
Professor of Electrical and Computer Engineering
Lawrence Carin earned the BS, MS, and PhD degrees in electrical engineering at the
University of Maryland, College Park, in 1985, 1986, and 1989, respectively. In 1989
he joined the Electrical Engineering Department at Polytechnic University (Brooklyn)
as an Assistant Professor, and became an Associate Professor there in 1994. In September
1995 he joined the Electrical and Computer Engineering (ECE) Department at Duke University,
where he is now a Professor. He was ECE Department Chair from 2011
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