  Exponential is a basic signal form, and how to fast acquire this signal is
one of the fundamental problems and frontiers in signal processing. To achieve
this goal, partial data may be acquired but result in the severe artifacts in
its spectrum, which is the Fourier transform of exponentials. Thus, reliable
spectrum reconstruction is highly expected in the fast sampling in many
applications, such as chemistry, biology, and medical imaging. In this work, we
propose a deep learning method whose neural network structure is designed by
unrolling the iterative process in the model-based state-of-the-art
exponentials reconstruction method with low-rank Hankel matrix factorization.
With the experiments on synthetic data and realistic biological magnetic
resonance signals, we demonstrate that the new method yields much lower
reconstruction errors and preserves the low-intensity signals much better.
