Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D ≥ 2) off-the-grid frequencies

Weiyu Xu, Jian Feng Cai, Kumar Vijay Mishra, Myung (Michael) Cho, Anton Kruger

Research output: Contribution to conferencePaper

42 Scopus citations

Abstract

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in [1] to recover 1-dimensional spectrally sparse signal. However, in spite of existing research efforts [2], it was still an open problem how to formulate an equivalent positive semidefinite program for atomic norm minimization in recovering signals with d-dimensional (d ≥ 2) off-the-grid frequencies. In this paper, we settle this problem by proposing equivalent semidefinite programming formulations of atomic norm minimization to recover signals with d-dimensional (d ≥ 2) off-the-grid frequencies.

Original languageEnglish (US)
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE Information Theory and Applications Workshop, ITA 2014 - San Diego, CA, United States
Duration: Feb 9 2014Feb 14 2014

Other

Other2014 IEEE Information Theory and Applications Workshop, ITA 2014
CountryUnited States
CitySan Diego, CA
Period2/9/142/14/14

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Information Systems

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    Xu, W., Cai, J. F., Mishra, K. V., Cho, M. M., & Kruger, A. (2014). Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D ≥ 2) off-the-grid frequencies. Paper presented at 2014 IEEE Information Theory and Applications Workshop, ITA 2014, San Diego, CA, United States. https://doi.org/10.1109/ITA.2014.6804267