Deterministic Matrices with a Restricted Isometry Property for Partially Structured Sparse Signals

Alihan Kaplan, Volker Pohl, Holger Boche

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

3 Scopus citations

Abstract

Compressive sampling has become an important tool in diverse applications. One of its main challenges, the construction of deterministic sensing matrices with restricted isometry property (RIP) in the optimal sparsity regime, is still an open problem, despite being of crucial importance for practical system designs. The only known work constructing deterministic RIP matrices beyond the square root bottleneck is due to Bourgain et al. The aim of this paper is to construct sensing matrices consisting of two orthogonal bases and to analyse their RIP properties based on the flat-RIP. Using a known estimation on exponential sums due to Karatsuba, we deduce an RIP result for signals which are restricted to a certain sparse structure. Without any assumption on the sparsity structure, we end up facing a known open problem from number theory regarding exponential sums.

Original languageEnglish
Title of host publication2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728137414
DOIs
StatePublished - Jul 2019
Event13th International Conference on Sampling Theory and Applications, SampTA 2019 - Bordeaux, France
Duration: 8 Jul 201912 Jul 2019

Publication series

Name2019 13th International Conference on Sampling Theory and Applications, SampTA 2019

Conference

Conference13th International Conference on Sampling Theory and Applications, SampTA 2019
Country/TerritoryFrance
CityBordeaux
Period8/07/1912/07/19

Keywords

  • deterministic compressive sampling
  • flat restricted isometry property
  • structured sparsity

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