Construction of incoherent unit norm tight frames with application to compressed sensing

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

Research output: Contribution to journalArticle

39 Scopus citations

Abstract

Despite the important properties of unit norm tight frames (UNTFs) and equiangular tight frames (ETFs), their construction has been proven extremely difficult. The few known techniques produce only a small number of such frames while imposing certain restrictions on frame dimensions. Motivated by the application of incoherent tight frames in compressed sensing (CS), we propose a methodology to construct incoherent UNTFs. When frame redundancy is not very high, the achieved maximal column correlation becomes close to the lowest possible bound. The proposed methodology may construct frames of any dimensions. The obtained frames are employed in CS to produce optimized projection matrices. Experimental results show that the proposed optimization technique improves CS signal recovery, increasing the reconstruction accuracy. Considering that the UNTFs and ETFs are important in sparse representations, channel coding, and communications, we expect that the proposed construction will be useful in other applications, besides the CS.

Original languageEnglish (US)
Article number6748087
Pages (from-to)2319-2330
Number of pages12
JournalIEEE Transactions on Information Theory
Volume60
Issue number4
DOIs
StatePublished - Jan 1 2014

Keywords

  • Grassmannian frames
  • Unit norm tight frames
  • compressed sensing

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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