  Undersampling can accelerate the signal acquisition but at the cost of
bringing in artifacts. Removing these artifacts is a fundamental problem in
signal processing and this task is also called signal reconstruction. Through
modeling signals as the superimposed exponential functions, deep learning has
achieved fast and high-fidelity signal reconstruction by training a mapping
from the undersampled exponentials to the fully sampled ones. However, the
mismatch, such as the sampling rate of undersampling, the organ and the
contrast of imaging, between the training and target data will heavily
compromise the reconstruction. To address this issue, we propose Alternating
Deep Low-Rank (ADLR), which combines deep learning solvers and classic
optimization solvers. Experiments on the reconstruction of synthetic and
realistic biomedical magnetic resonance signals demonstrate that ADLR can
effectively mitigate the mismatch issue and achieve lower reconstruction errors
than state-of-the-art methods.
