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PRECISE SEMIDEFINITE PROGRAMMING FORMULATION OF ATOMIC NORM MINIMIZATION FOR RECOVERING D-DIMENSIONAL (D ≥ 2) OFF-THE-GRID FREQUENCIES
| Citations: | 4 - 2 self |
BibTeX
@MISC{Xu_precisesemidefinite,
author = {Weiyu Xu and Jian-feng Cai and Kumar Vijay Mishra and Myung Cho and Anton Kruger},
title = {PRECISE SEMIDEFINITE PROGRAMMING FORMULATION OF ATOMIC NORM MINIMIZATION FOR RECOVERING D-DIMENSIONAL (D ≥ 2) OFF-THE-GRID FREQUENCIES},
year = {}
}
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Abstract
Recent research in off-the-grid compressed sensing (CS) has demon-strated 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 min-imization 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. Index Terms — compressed sensing, spectral estimation, matrix completion, sum of squares 1.
Keyphrases
off-the-grid frequency recovering d-dimensional atomic norm minimization sparse signal index term recent research open problem spectral estimation time-domain sample atomic norm min-imization equivalent positive semidefinite program matrix completion off-the-grid compressed sensing certain condition research effort
