Physics-Informed Sylvester Normalizing Flows for Bayesian Inference in Magnetic Resonance Spectroscopy

TL;DR

This paper presents a physics-informed Bayesian inference method using Sylvester normalizing flows to improve metabolite quantification in magnetic resonance spectroscopy, addressing challenges like spectral overlap and noise.

Contribution

It introduces a novel physics-informed SNF-based framework for more accurate and reliable Bayesian metabolite quantification in MRS, incorporating prior knowledge of signal formation.

Findings

Accurate metabolite quantification on simulated 7T MRS data

Well-calibrated uncertainties and parameter correlation insights

Effective handling of multi-modal distributions

Abstract

Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the Cram\'er-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.