Paper Info
Title
Communications-Inspired Projection Design with Application to Compressive Sensing
Abstract
We consider the recovery of an underlying signal x is an element of C-m based on projection measurements of the form y = Mx + w, where y is an element of C-l 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 similar to CN(w; 0, Sigma(w)) for known Sigma(w). The objective is to design a projection matrix M is an element of C-lxm to maximize key information-theoretic quantities with operational significance, including the mutual information between the signal and the projections I(x; y) or the Renyi entropy of the projections h(alpha) (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 Renyi 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.
Year
DOI
Venue
2012
10.1137/120878380
SIAM JOURNAL ON IMAGING SCIENCES
Keywords
DocType
Volume
low resolution imaging,compressed sensing,MIMO communication,precoder design,mode alignment,mutual information
Journal
5
Issue
ISSN
Citations 
4
1936-4954
37
PageRank 
References 
Authors
1.33
28
5
Name
Order
Citations
PageRank
William R. Carson1533.34
Minhua Chen2492.22
Miguel R. D. Rodrigues31500111.23
A. R. Calderbank4125502208.54
L. Carin54603339.36