Paper Info
Title
Demixing Sines And Spikes: Robust Spectral Super-Resolution In The Presence Of Outliers
Abstract
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.
Year
DOI
Venue
2016
10.1093/imaiai/iax005
INFORMATION AND INFERENCE-A JOURNAL OF THE IMA
Keywords
Field
DocType
atomic norm, continuous dictionary, convex optimization, greedy methods, line spectra estimation, outliers, semi-definite programming, sparse recovery, super-resolution
Noise reduction,Mathematical optimization,Finite set,Outlier,Spectral line,Regular polygon,Logarithm,Mathematics,Perturbation (astronomy),Semidefinite programming
Journal
Volume
Issue
ISSN
7
1
2049-8764
Citations 
PageRank 
References 
1
0.37
0
Authors
4
Name
Order
Citations
PageRank
Carlos Fernandez-Granda115413.21
Gongguo Tang250536.29
Xiaodong Wang33958310.41
Le Zheng4849.88