Math @ Duke

Publications [#235786] of Robert Calderbank
Papers Published
 Carson, WR; Chen, M; Rodrigues, MRD; Calderbank, R; Carin, L, CommunicationsInspired Projection Design with Application to Compressive Sensing,
Siam Journal on Imaging Sciences, vol. 5 no. 4
(January, 2012),
pp. 11851212, ISSN 19364954 [repository], [doi]
(last updated on 2018/10/20)
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 informationtheoretic 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 wellknown 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 stateoftheart adaptive CS signal recovery is achieved. © 2012 Society for Industrial and Applied Mathematics.


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