Off-Grid Frequency Estimation with Random Measurements

Xushan CHEN; Jibin YANG; Meng SUN; Jianfeng LI

doi:10.1587/transfun.E100.A.2493

Off-Grid Frequency Estimation with Random Measurements

Xushan CHEN, Jibin YANG, Meng SUN, Jianfeng LI

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In order to significantly reduce the time and space needed, compressive sensing builds upon the fundamental assumption of sparsity under a suitable discrete dictionary. However, in many signal processing applications there exists mismatch between the assumed and the true sparsity bases, so that the actual representative coefficients do not lie on the finite grid discretized by the assumed dictionary. Unlike previous work this paper introduces the unified compressive measurement operator into atomic norm denoising and investigates the problems of recovering the frequency support of a combination of multiple sinusoids from sub-Nyquist samples. We provide some useful properties to ensure the optimality of the unified framework via semidefinite programming (SDP). We also provide a sufficient condition to guarantee the uniqueness of the optimizer with high probability. Theoretical results demonstrate the proposed method can locate the nonzero coefficients on an infinitely dense grid over a wide range of SNR case.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.11 pp.2493-2497

Publication Date: 2017/11/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2493

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Xushan CHEN
  National Defence University of PLA
Jibin YANG
  PLA University of Science and Technology
Meng SUN
  PLA University of Science and Technology
Jianfeng LI
  National Defence University of PLA

Keyword

compressive sensing, frequency estimation, random measurement, atomic norm, semidefinite programming

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Xushan CHEN, Jibin YANG, Meng SUN, Jianfeng LI, "Off-Grid Frequency Estimation with Random Measurements" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 11, pp. 2493-2497, November 2017, doi: 10.1587/transfun.E100.A.2493.
Abstract: In order to significantly reduce the time and space needed, compressive sensing builds upon the fundamental assumption of sparsity under a suitable discrete dictionary. However, in many signal processing applications there exists mismatch between the assumed and the true sparsity bases, so that the actual representative coefficients do not lie on the finite grid discretized by the assumed dictionary. Unlike previous work this paper introduces the unified compressive measurement operator into atomic norm denoising and investigates the problems of recovering the frequency support of a combination of multiple sinusoids from sub-Nyquist samples. We provide some useful properties to ensure the optimality of the unified framework via semidefinite programming (SDP). We also provide a sufficient condition to guarantee the uniqueness of the optimizer with high probability. Theoretical results demonstrate the proposed method can locate the nonzero coefficients on an infinitely dense grid over a wide range of SNR case.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2493/_p

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@ARTICLE{e100-a_11_2493,
author={Xushan CHEN, Jibin YANG, Meng SUN, Jianfeng LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Off-Grid Frequency Estimation with Random Measurements},
year={2017},
volume={E100-A},
number={11},
pages={2493-2497},
abstract={In order to significantly reduce the time and space needed, compressive sensing builds upon the fundamental assumption of sparsity under a suitable discrete dictionary. However, in many signal processing applications there exists mismatch between the assumed and the true sparsity bases, so that the actual representative coefficients do not lie on the finite grid discretized by the assumed dictionary. Unlike previous work this paper introduces the unified compressive measurement operator into atomic norm denoising and investigates the problems of recovering the frequency support of a combination of multiple sinusoids from sub-Nyquist samples. We provide some useful properties to ensure the optimality of the unified framework via semidefinite programming (SDP). We also provide a sufficient condition to guarantee the uniqueness of the optimizer with high probability. Theoretical results demonstrate the proposed method can locate the nonzero coefficients on an infinitely dense grid over a wide range of SNR case.},
keywords={},
doi={10.1587/transfun.E100.A.2493},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - Off-Grid Frequency Estimation with Random Measurements
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2493
EP - 2497
AU - Xushan CHEN
AU - Jibin YANG
AU - Meng SUN
AU - Jianfeng LI
PY - 2017
DO - 10.1587/transfun.E100.A.2493
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2017
AB - In order to significantly reduce the time and space needed, compressive sensing builds upon the fundamental assumption of sparsity under a suitable discrete dictionary. However, in many signal processing applications there exists mismatch between the assumed and the true sparsity bases, so that the actual representative coefficients do not lie on the finite grid discretized by the assumed dictionary. Unlike previous work this paper introduces the unified compressive measurement operator into atomic norm denoising and investigates the problems of recovering the frequency support of a combination of multiple sinusoids from sub-Nyquist samples. We provide some useful properties to ensure the optimality of the unified framework via semidefinite programming (SDP). We also provide a sufficient condition to guarantee the uniqueness of the optimizer with high probability. Theoretical results demonstrate the proposed method can locate the nonzero coefficients on an infinitely dense grid over a wide range of SNR case.
ER -