Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction

Applied and Computational Harmonic Analysis
Jian-Feng CaiGui-Bo Ye

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(Rln(2)N). 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 demonstra...Continue Reading

References

Oct 31, 2007·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Michael LustigJohn M Pauly
Nov 13, 2014·Angewandte Chemie·Xiaobo QuVladislav Orekhov

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Citations

Oct 29, 2017·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Peng CaoPeder E Z Larson
May 27, 2016·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Peng CaoPeder E Z Larson

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