# Exponential Signal Reconstruction with Deep Hankel Matrix Factorization

arXiv: https://arxiv.org/abs/2007.06246 · HTML: https://mlsanity.com/paper/2007.06246/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Physics-driven Synthetic Data Learning for Biomedical Magnetic Resonance](https://mlsanity.com/paper/2203.11178/) (2022)
- [Deep Manifold Learning for Dynamic MR Imaging](https://mlsanity.com/paper/2104.01102/) (2021)
- [Magnetic Resonance Spectroscopy Quantification Aided by Deep Estimations of Imperfection Factors and Macromolecular Signal](https://mlsanity.com/paper/2306.09681/) (2023)
- [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)
- [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)
- [Unsupervised Unfolded rPCA (U2-rPCA): Deep Interpretable Clutter Filtering for Ultrasound Microvascular Imaging](https://mlsanity.com/paper/2510.00660/) (2025)

## Abstract (arXiv)

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.