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

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Citation Author(s):
Submitted by:
Qiuwei Li
Last updated:
10 December 2016 - 3:39pm
Document Type:
Presentation Slides
Document Year:
2016
Event:
Presenters Name:
Qiuwei Li
Paper Code:
1306

Abstract 

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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