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.

### Paper Details

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- Submitted On:
- 10 December 2016 - 3:39pm
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- Type:
- Presentation Slides
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- Presenter's Name:
- Qiuwei Li
- Paper Code:
- 1306
- Document Year:
- 2016
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url = {http://sigport.org/1383},

author = { },

publisher = {IEEE SigPort},

title = {Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision},

year = {2016} }

T1 - Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision

AU -

PY - 2016

PB - IEEE SigPort

UR - http://sigport.org/1383

ER -