摘要
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a sinusoidal and a sparse component. We propose to demix the two components and super-resolve the spectrum of the multisinusoidal signal by solving a convex program. Our main theoretical result is that-up to logarithmic factors-this approach is guaranteed to be successful with high probability for a number of spectral lines that is linear in the number of measurements, even if a constant fraction of the data are outliers. The result holds under the assumption that the phases of the sinusoidal and sparse components are random and the line spectrum satisfies a minimum-separation condition. We show that the method can be implemented via semi-definite programming, and explain how to adapt it in the presence of dense perturbations as well as exploring its connection to atomic-norm denoising. In addition, we propose a fast greedy demixing method that provides good empirical results when coupled with a local non-convex-optimization step.
源语言 | 英语 |
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页(从-至) | 105-168 |
页数 | 64 |
期刊 | Information and Inference |
卷 | 7 |
期 | 1 |
DOI | |
出版状态 | 已出版 - 15 3月 2018 |
已对外发布 | 是 |