期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 66, 期 21, 页码 5520-5533出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2018.2869122
关键词
Exponential signal; low rank; Hankel matrix completion; spectrally sparse signal; Vandermonde factorization
资金
- National Natural Science Foundation of China [61571380, 61811530021, 61871341, U1632274, 61672335, 61601276]
- Natural Science Foundation of Fujian Province of China [2018J06018, 2016J05205]
- Fundamental Research Funds for the Central Universities [20720150109]
- Science and Technology Program of Xiamen [3502Z20183053]
- Hong Kong Research Grant Council [16300616]
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-norm-minimization-based Hankel matrix completion method, while it 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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