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Communications-inspired projection design with application to compressive sensing

dc.contributor.author Calderbank, R
dc.contributor.author Carin, Lawrence
dc.contributor.author Carson, WR
dc.contributor.author Chen, M
dc.contributor.author Rodrigues, Miguel
dc.date.accessioned 2014-07-22T16:18:12Z
dc.date.issued 2012-12-01
dc.identifier.uri http://hdl.handle.net/10161/8952
dc.description.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.
dc.relation.ispartof SIAM Journal on Imaging Sciences
dc.relation.isversionof 10.1137/120878380
dc.title Communications-inspired projection design with application to compressive sensing
dc.type Journal article
pubs.begin-page 1182
pubs.end-page 1212
pubs.issue 4
pubs.organisational-group Computer Science
pubs.organisational-group Duke
pubs.organisational-group Electrical and Computer Engineering
pubs.organisational-group Mathematics
pubs.organisational-group Physics
pubs.organisational-group Pratt School of Engineering
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 5
dc.identifier.eissn 1936-4954


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