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arXiv · 1809.00750

Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery -- Application in Fast NMR Spectroscopy

Jiaxi Ying·Jian-Feng Cai·Di Guo·Gongguo Tang·Zhong Chen·Xiaobo Qu
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Abstract

Many signals are modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. This paper studies the problem of recovering exponential signals from a random subset of samples. We exploit the Vandermonde structure of the Hankel matrix formed by the exponential signal and formulate signal recovery as Hankel matrix completion with Vandermonde factorization (HVaF). A numerical algorithm is developed to solve the proposed model and its sequence convergence is analyzed theoretically. Experiments on synthetic data demonstrate that HVaF succeeds over a wider regime than the state-of-the-art nuclear-normminimization-based Hankel matrix completion method, while has a less restriction on frequency separation than the state-of-the-art atomic norm minimization and fast iterative hard thresholding methods. The effectiveness of HVaF is further validated on biological magnetic resonance spectroscopy data.

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Jiaxi Ying, Jian-Feng Cai, Di Guo, Gongguo Tang, Zhong Chen, Xiaobo Qu. 2018-09-04. Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery -- Application in Fast NMR Spectroscopy. https://doi.org/10.1109/tsp.2018.2869122

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