A Theory of Computational Resolution Limit for Line Spectral Estimation

Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this...

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Published inIEEE transactions on information theory Vol. 67; no. 7; pp. 4812 - 4827
Main Authors Liu, Ping, Zhang, Hai
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Estimation
Extraterrestrial measurements
Line spectra
Line spectral estimation
Minimization
Noise level
Phase measurement
phase transition
Phase transitions
Pollution measurement
Random noise
Recovery
resolution limit
Separation
Signal processing
Signal to noise ratio
Online AccessGet full text
ISSN0018-9448
1557-9654
DOI10.1109/TIT.2021.3075149

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Abstract Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this paper, we introduce and quantitatively characterize the two resolution limits for the line spectral estimation problem under deterministic noise: one is the minimum separation distance between the line spectra that is required for exact detection of their number, and the other is the minimum separation distance between the line spectra that is required for a stable recovery of their supports. The quantitative results imply a phase transition phenomenon in each of the two recovery problems, and also the subtle difference between the two. We further propose a sweeping singular-value-thresholding algorithm for the number detection problem and conduct numerical experiments. The numerical results confirm the phase transition phenomenon in the number detection problem.
AbstractList Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the theoretical understanding of this problem is still elusive. In this paper, we introduce and quantitatively characterize the two resolution limits for the line spectral estimation problem under deterministic noise: one is the minimum separation distance between the line spectra that is required for exact detection of their number, and the other is the minimum separation distance between the line spectra that is required for a stable recovery of their supports. The quantitative results imply a phase transition phenomenon in each of the two recovery problems, and also the subtle difference between the two. We further propose a sweeping singular-value-thresholding algorithm for the number detection problem and conduct numerical experiments. The numerical results confirm the phase transition phenomenon in the number detection problem.
Author Liu, Ping
Zhang, Hai
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SubjectTerms Algorithms
Estimation
Extraterrestrial measurements
Line spectra
Line spectral estimation
Minimization
Noise level
Phase measurement
phase transition
Phase transitions
Pollution measurement
Random noise
Recovery
resolution limit
Separation
Signal processing
Signal to noise ratio
Title A Theory of Computational Resolution Limit for Line Spectral Estimation
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