  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.
