Recovery guarantees for Compressed Sensing with unknown errors

Simone Brugiapaglia, Ben Adcock, Richard K. Archibald

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

From a numerical analysis perspective, assessing the robustness of ℓ1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori estimates of the noise, which can be very hard to obtain in practice, especially when the noise term also includes unknown discrepancies between the finite model and data. In this work, we study the performance of ℓ1-minimization when these estimates are not available, providing robust recovery guarantees for quadratically constrained basis pursuit and random sampling in bounded orthonormal systems. Several applications of this work are approximation of high-dimensional functions, infinite-dimensional sparse regularization for inverse problems, and fast algorithms for non-Cartesian Magnetic Resonance Imaging.

Original languageEnglish
Title of host publication2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
EditorsGholamreza Anbarjafari, Andi Kivinukk, Gert Tamberg
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages533-537
Number of pages5
ISBN (Electronic)9781538615652
DOIs
StatePublished - Sep 1 2017
Event12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia
Duration: Jul 3 2017Jul 7 2017

Publication series

Name2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

Conference

Conference12th International Conference on Sampling Theory and Applications, SampTA 2017
Country/TerritoryEstonia
CityTallinn
Period07/3/1707/7/17

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