Approximate equiangular tight frames for compressed sensing and CDMA applications

Evaggelia Tsiligianni, Lisimachos P. Kondi*, Aggelos K. Katsaggelos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Performance guarantees for recovery algorithms employed in sparse representations, and compressed sensing highlights the importance of incoherence. Optimal bounds of incoherence are attained by equiangular unit norm tight frames (ETFs). Although ETFs are important in many applications, they do not exist for all dimensions, while their construction has been proven extremely difficult. In this paper, we construct frames that are close to ETFs. According to results from frame and graph theory, the existence of an ETF depends on the existence of its signature matrix, that is, a symmetric matrix with certain structure and spectrum consisting of two distinct eigenvalues. We view the construction of a signature matrix as an inverse eigenvalue problem and propose a method that produces frames of any dimensions that are close to ETFs. Due to the achieved equiangularity property, the so obtained frames can be employed as spreading sequences in synchronous code-division multiple access (s-CDMA) systems, besides compressed sensing.

Original languageEnglish (US)
Article number66
JournalEurasip Journal on Advances in Signal Processing
Volume2017
Issue number1
DOIs
StatePublished - Dec 1 2017

Keywords

  • Compressed sensing
  • Equiangular unit norm tight frames
  • Signature matrix
  • Spreading sequences

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems
  • Hardware and Architecture
  • Electrical and Electronic Engineering

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