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Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision

Abstract: 

This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes from noisy observations. When the Signal-to-Noise Ratio is reasonably high and the true frequencies are separated by $O(\frac{1}{n})$, the atomic norm estimator is shown to localize the correct number of frequencies, each within a neighborhood of size $O(\sqrt{\frac{\log n}{n^3}} \sigma)$ of one of the true frequencies. Here $n$ is half the number of temporal samples and $\sigma^2$ is the Gaussian noise variance. The analysis is based on a primal-dual witness construction procedure. The obtained error bound matches the Cram\'er-Rao lower bound up to a logarithmic factor. The relationship between resolution (separation of frequencies) and precision or accuracy of the estimator is highlighted.

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Paper Details

Authors:
Submitted On:
10 December 2016 - 3:39pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Qiuwei Li
Paper Code:
1306
Document Year:
2016
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Document Files

Slides_GlobalSIP.pdf

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[1] , "Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1383. Accessed: Sep. 20, 2020.
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publisher = {IEEE SigPort},
title = {Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision},
year = {2016} }
TY - EJOUR
T1 - Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision
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PY - 2016
PB - IEEE SigPort
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. (2016). Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision. IEEE SigPort. http://sigport.org/1383
, 2016. Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision. Available at: http://sigport.org/1383.
. (2016). "Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision." Web.
1. . Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1383