Journal article
Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction
Applied and computational harmonic analysis, Vol.41(2), pp.470-490
09/2016
DOI: 10.1016/j.acha.2016.02.003
PMCID: PMC5662150
PMID: 29093630
Abstract
This paper explores robust recovery of a superposition of R distinct complex exponential functions with or without damping factors from a few random Gaussian projections. We assume that the signal of interest is of 2N−1 dimensions and R<2N−1. This framework covers a large class of signals arising from real applications in biology, automation, imaging science, etc. To reconstruct such a signal, our algorithm is to seek a low-rank Hankel matrix of the signal by minimizing its nuclear norm subject to the consistency on the sampled data. Our theoretical results show that a robust recovery is possible as long as the number of projections exceeds O(Rln2N). No incoherence or separation condition is required in our proof. Our method can be applied to spectral compressed sensing where the signal of interest is a superposition of R complex sinusoids. Compared to existing results, our result here does not need any separation condition on the frequencies, while achieving better or comparable bounds on the number of measurements. Furthermore, our method provides theoretical guidance on how many samples are required in the state-of-the-art non-uniform sampling in NMR spectroscopy. The performance of our algorithm is further demonstrated by numerical experiments.
Details
- Title: Subtitle
- Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction
- Creators
- Jian-Feng Cai - Hong Kong University of Science and TechnologyXiaobo Qu - Xiamen UniversityWeiyu Xu - University of IowaGui-Bo Ye - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Applied and computational harmonic analysis, Vol.41(2), pp.470-490
- DOI
- 10.1016/j.acha.2016.02.003
- PMID
- 29093630
- PMCID
- PMC5662150
- NLM abbreviation
- Appl Comput Harmon Anal
- ISSN
- 1063-5203
- eISSN
- 1096-603X
- Publisher
- Elsevier Inc
- Grant note
- 20720150109 / Fundamental Research Funds for the Central Universities DMS-1418737 / NSF (http://dx.doi.org/10.13039/100000001) 61571380; 61201045 / National Natural Science Foundation of China (http://dx.doi.org/10.13039/501100001809) OCRF-2014-CRG-3 / KAUST 1R01EB020665-01 / NIH (http://dx.doi.org/10.13039/100000002) 318608 / Simons Foundation (http://dx.doi.org/10.13039/100000893) OG-15-001 / Iowa Energy Center
- Language
- English
- Date published
- 09/2016
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984197264802771
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