Non-Gaussian observations in nonlinear compressed sensing via Stein discrepancies. (21st May 2018)

• Record Type: Journal Article
• Authors: Goldstein, Larry; Wei, Xiaohan
• Is Part Of: Information and inference. Volume 8:Number 1(2019)
• Page Start: 125
• Page End: 159
• Publication Date: 2018-05-21
• Subjects: signal reconstruction -- semi-parametric single-index model -- Stein coefficient -- zero-bias coupling -- generic chaining; Mathematical models -- Periodicals; 519.605
• DOI: 10.1093/imaiai/iay006
• Languages: English
• ISSNs: 2049-8764

Abstract

Abstract: Performance guarantees for estimates of unknowns in nonlinear compressed sensing models under non-Gaussian measurements can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the value of zero under Gaussian or linear sensing. The use of these characteristics, or discrepancies, improves some previous results in this area by relaxing conditions and tightening performance bounds. In addition, these characteristics are tractable to compute when Gaussian sensing is corrupted by either additive errors or mixing.