A Sparse Model-inspired Deep Thresholding Network for Exponential Signal Reconstruction -- Application in Fast Biological Spectroscopy

TL;DR

This paper introduces MoDern, a deep learning model inspired by sparse optimization, for fast and robust exponential signal reconstruction, demonstrating superior performance and generalization in biological spectroscopy applications.

Contribution

It presents a novel deep neural network architecture combining sparse model optimization with learnable thresholding, trained on synthetic data, for improved spectral reconstruction.

Findings

MoDern outperforms existing methods in accuracy and speed.

It generalizes well from synthetic to biological data.

The model has a small parameter count and is easy to deploy.

Abstract

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.