Journal article
Spectral Super-Resolution With Prior Knowledge
IEEE transactions on signal processing, Vol.63(20), pp.5342-5357
10/2015
DOI: 10.1109/TSP.2015.2452223
Abstract
We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is often known. The prior information might be simply knowing precisely some signal frequencies or the likelihood of a particular frequency component in the signal. We devise a general semidefinite program to recover these frequencies using theories of positive trigonometric polynomials. Our theoretical analysis shows that, given sufficient prior information, perfect signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies. Numerical experiments demonstrate great performance enhancements using our method. We show that the nominal resolution necessary for the grid-free results can be improved if prior information is suitably employed.
Details
- Title: Subtitle
- Spectral Super-Resolution With Prior Knowledge
- Creators
- Kumar Vijay Mishra - University of IowaMyung Cho - University of IowaAnton Kruger - University of IowaWeiyu Xu - University of Iowa
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on signal processing, Vol.63(20), pp.5342-5357
- DOI
- 10.1109/TSP.2015.2452223
- ISSN
- 1053-587X
- eISSN
- 1941-0476
- Language
- English
- Date published
- 10/2015
- Academic Unit
- Electrical and Computer Engineering; Civil and Environmental Engineering
- Record Identifier
- 9984197062002771
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