Guaranteed Sparse Signal Recovery with Highly Coherent Sensing Matrices

Authors

Guangliang Chen, Claremont McKenna CollegeFollow
Atul Divekar, Alcatel-Lucent
Deanna Needell, Claremont McKenna CollegeFollow

Document Type

Article - postprint

Department

Mathematics (CMC)

Publication Date

4-1-2014

Abstract

Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling matrices such as Gaussian and Bernoulli matrices. In common physically feasible signal acquisition and reconstruction scenarios such as super-resolution of images, the sensing matrix has a non-random structure with highly correlated columns. Here we present a compressive sensing type recovery algorithm, called Partial Inversion (PartInv), that overcomes the correlations among the columns. We provide theoretical justification as well as empirical comparisons.

Rights Information

© 2014 Sampling Theory in Signal Analysis and Image Processing

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Chen, G., Divekar, A., Needell, D., "Guaranteed sparse signal recovery with highly coherent sensing matrices", Sampling Theory in Signal Analysis and Image Processing, To appear, arXiv:1311.0314v2, 2013.