Exponential Signal Reconstruction with Deep Hankel Matrix Factorization

TL;DR

This paper introduces a deep learning approach for fast exponential signal reconstruction that unrolls an iterative low-rank Hankel matrix factorization process, significantly improving accuracy in spectrum recovery from partial data.

Contribution

The paper presents a novel deep neural network architecture based on unrolling an iterative low-rank Hankel matrix factorization method for exponential signal reconstruction.

Findings

Lower reconstruction errors on synthetic data

Better preservation of low-intensity signals in MRI

Effective in biological magnetic resonance signals

Abstract

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.