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

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.

arXiv comment14 pages, 9 figures, 3 tables, 63 references

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Cited by in corpus (3)

• A Unified Framework for Structured Graph Learning via Spectral Constraints
• A Sparse Model-inspired Deep Thresholding Network for Exponential Signal Reconstruction -- Application in Fast Biological Spectroscopy
• An auto-parameter denoising method for nuclear magnetic resonance spectroscopy based on low-rank Hankel matrix