  The non-uniform sampling is a powerful approach to enable fast acquisition
but requires sophisticated reconstruction algorithms. Faithful reconstruction
from partial sampled exponentials is highly expected in general signal
processing and many applications. Deep learning has shown astonishing potential
in this field but many existing problems, such as lack of robustness and
explainability, greatly limit its applications. In this work, by combining
merits of the sparse model-based optimization method and data-driven deep
learning, we propose a deep learning architecture for spectra reconstruction
from undersampled data, called MoDern. It follows the iterative reconstruction
in solving a sparse model to build the neural network and we elaborately design
a learnable soft-thresholding to adaptively eliminate the spectrum artifacts
introduced by undersampling. Extensive results on both synthetic and biological
data show that MoDern enables more robust, high-fidelity, and ultra-fast
reconstruction than the state-of-the-art methods. Remarkably, MoDern has a
small number of network parameters and is trained on solely synthetic data
while generalizing well to biological data in various scenarios. Furthermore,
we extend it to an open-access and easy-to-use cloud computing platform
(XCloud-MoDern), contributing a promising strategy for further development of
biological applications.
