Spectral Super-Resolution With Prior Knowledge

Kumar Vijay Mishra, Myung Cho, Anton Kruger, Weiyu Xu

Research output: Contribution to journalArticle

26 Scopus citations

Abstract

We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is often known. The prior information might be simply knowing precisely some signal frequencies or the likelihood of a particular frequency component in the signal. We devise a general semidefinite program to recover these frequencies using theories of positive trigonometric polynomials. Our theoretical analysis shows that, given sufficient prior information, perfect signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies. Numerical experiments demonstrate great performance enhancements using our method. We show that the nominal resolution necessary for the grid-free results can be improved if prior information is suitably employed.

Original languageEnglish (US)
Article number7145484
Pages (from-to)5342-5357
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume63
Issue number20
DOIs
StatePublished - Oct 15 2015

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

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