# Accelerated Magnetic Resonance Spectroscopy with Vandermonde Factorization

## TL;DR

This paper introduces a Vandermonde factorization-based reconstruction method for multi-dimensional magnetic resonance spectroscopy, significantly reducing data acquisition time while maintaining high spectral fidelity.

## Contribution

The proposed method leverages the exponential structure of MR signals, outperforming existing low-rank Hankel matrix techniques in spectrum reconstruction accuracy.

## Key findings

- Achieves faithful spectrum reconstruction on synthetic data.
- Outperforms state-of-the-art low rank Hankel matrix methods.
- Reduces data acquisition time in MR spectroscopy.

## Abstract

Multi-dimensional magnetic resonance spectroscopy is an important tool for studying molecular structures, interactions and dynamics in bio-engineering. The data acquisition time, however, is relatively long and non-uniform sampling can be applied to reduce this time. To obtain the full spectrum,a reconstruction method with Vandermonde factorization is proposed.This method explores the general signal property in magnetic resonance spectroscopy: Its time domain signal is approximated by a sum of a few exponentials. Results on synthetic and realistic data show that the new approach can achieve faithful spectrum reconstruction and outperforms state-of-the-art low rank Hankel matrix method.