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Communications-inspired projection design with application to compressive sensing

Publication ,  Journal Article
Carson, WR; Chen, M; Rodrigues, MRD; Calderbank, R; Carin, L
Published in: SIAM Journal on Imaging Sciences
January 1, 2012

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.

Duke Scholars

Published In

SIAM Journal on Imaging Sciences

DOI

EISSN

1936-4954

Publication Date

January 1, 2012

Volume

5

Issue

4

Start / End Page

1182 / 1212

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4901 Applied mathematics
  • 4603 Computer vision and multimedia computation
 

Citation

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Carson, W. R., Chen, M., Rodrigues, M. R. D., Calderbank, R., & Carin, L. (2012). Communications-inspired projection design with application to compressive sensing. SIAM Journal on Imaging Sciences, 5(4), 1182–1212. https://doi.org/10.1137/120878380
Carson, W. R., M. Chen, M. R. D. Rodrigues, R. Calderbank, and L. Carin. “Communications-inspired projection design with application to compressive sensing.” SIAM Journal on Imaging Sciences 5, no. 4 (January 1, 2012): 1182–1212. https://doi.org/10.1137/120878380.
Carson WR, Chen M, Rodrigues MRD, Calderbank R, Carin L. Communications-inspired projection design with application to compressive sensing. SIAM Journal on Imaging Sciences. 2012 Jan 1;5(4):1182–212.
Carson, W. R., et al. “Communications-inspired projection design with application to compressive sensing.” SIAM Journal on Imaging Sciences, vol. 5, no. 4, Jan. 2012, pp. 1182–212. Scopus, doi:10.1137/120878380.
Carson WR, Chen M, Rodrigues MRD, Calderbank R, Carin L. Communications-inspired projection design with application to compressive sensing. SIAM Journal on Imaging Sciences. 2012 Jan 1;5(4):1182–1212.

Published In

SIAM Journal on Imaging Sciences

DOI

EISSN

1936-4954

Publication Date

January 1, 2012

Volume

5

Issue

4

Start / End Page

1182 / 1212

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4901 Applied mathematics
  • 4603 Computer vision and multimedia computation