On Compressive orthonormal Sensing

Yi Zhou, Huishuai Zhang, Yingbin Liang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

The Compressive Sensing (CS) approach for recovering sparse signal with orthonormal measurements has been studied under various notions of coherence. However, existing notions of coherence either do not exploit the structure of the underlying signal, or are too complicated to provide an explicit sampling scheme for all orthonormal basis sets. Consequently, there is lack of understanding of key factors that guide the sampling of CS with orthonormal measurements and achieve as low sample complexity as possible. In this paper, we introduce a new notion of π-coherence that exploits both the sparsity structure of the signal and the local coherence. Based on π-coherence, we propose a sampling scheme that is adapted to the underlying true signal and is applicable for CS under all orthonormal basis. Our scheme outperforms (up to a constant factor) existing sampling schemes for orthonormal measurements, and achieves a near-optimal sample complexity (up to certain logarithm factors) for several popular choices of orthonormal basis. Furthermore, we characterize the necessary conditions on the sampling schemes for CS with orthonormal measurements. We then propose a practical multi-phase implementation of our sampling scheme, and verify its advantage over existing sampling schemes via application to magnetic resonance imaging (MRI) in medical science.

Original languageEnglish (US)
Title of host publication54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages299-305
Number of pages7
ISBN (Electronic)9781509045495
DOIs
StatePublished - Feb 10 2017
Event54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States
Duration: Sep 27 2016Sep 30 2016

Other

Other54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
CountryUnited States
CityMonticello
Period9/27/169/30/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Hardware and Architecture
  • Control and Optimization

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