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

arXiv: https://arxiv.org/abs/2012.14830 · HTML: https://mlsanity.com/paper/2012.14830/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2020.

## Built on by (most cited first, 12 of 12)

- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [One-dimensional Deep Low-rank and Sparse Network for Accelerated MRI](https://mlsanity.com/paper/2112.04721/) (2021)
- [Physics-driven Synthetic Data Learning for Biomedical Magnetic Resonance](https://mlsanity.com/paper/2203.11178/) (2022)
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- [Magnetic Resonance Spectroscopy Quantification Aided by Deep Estimations of Imperfection Factors and Macromolecular Signal](https://mlsanity.com/paper/2306.09681/) (2023)
- [A Faithful Deep Sensitivity Estimation for Accelerated Magnetic Resonance Imaging](https://mlsanity.com/paper/2210.12723/) (2022)
- [Deep Separable Spatiotemporal Learning for Fast Dynamic Cardiac MRI](https://mlsanity.com/paper/2402.15939/) (2024)
- [A Dynamics Theory of Implicit Regularization in Deep Low-Rank Matrix Factorization](https://mlsanity.com/paper/2212.14150/) (2022)
- [CloudBrain-NMR: An Intelligent Cloud Computing Platform for NMR Spectroscopy Processing, Reconstruction and Analysis](https://mlsanity.com/paper/2309.07178/) (2023)
- [Magnetic Resonance Spectroscopy Deep Learning Denoising Using Few In Vivo Data](https://mlsanity.com/paper/2101.11442/) (2021)
- [Convex Dual Theory Analysis of Two-Layer Convolutional Neural Networks with Soft-Thresholding](https://mlsanity.com/paper/2304.06959/) (2023)
- [An artificially intelligent magnetic resonance spectroscopy quantification method: Comparison between QNet and LCModel on the cloud computing platform CloudBrain-MRS](https://mlsanity.com/paper/2503.04469/) (2025)

## Abstract (arXiv)

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.