Sparse Reconstruction Under Sensing Constraints: A Controlled Approach

Abstract

This paper considers a controlled approach to sparse reconstruction under sensing constraints that have been largely ignored in related work on compressive sensing and sparse recovery. The first constraint stems from the reduced number of degrees of freedom of actual information gathering systems, which imposes specific structures on the sensing matrix departing from the conventional random ensembles. The second limitation originates from the unknown statistical model of the corrupting noise. A controlled sensing approach is proposed to guide the collection of informative measurements given the constrained sensing structure. In the presence of additive noise with unknown statistics, the proposed approach is shown to yield stable recovery and dispenses with the usual de-noising requirements. In addition, a sequential implementation with a stopping rule is proposed, thereby reducing the sample complexity for a target performance in reconstruction.

Publication Date

2-10-2017

Publication Title

54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016

Number of Pages

292-298

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/ALLERTON.2016.7852243

Socpus ID

85015153790 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85015153790

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