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

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.

WAND: Wavelet Analysis-based Neural Decomposition of MRS Signals for Artifact Removal

Accurate quantification of metabolites in magnetic resonance spectroscopy (MRS) is challenged by low signal-to-noise ratio (SNR), overlapping metabolites, and various artifacts. Particularly, unknown and unparameterized baseline effects obscure the quantification of low-concentration metabolites, limiting MRS reliability. This paper introduces wavelet analysis-based neural decomposition (WAND), a novel data-driven method designed to decompose MRS signals into their constituent components: metabolite-specific signals, baseline, and artifacts. WAND takes advantage of the enhanced separability of these components within the wavelet domain. The method employs a neural network, specifically a U-Net architecture, trained to predict masks for wavelet coefficients obtained through the continuous wavelet transform. These masks effectively isolate desired signal components in the wavelet domain, which are then inverse-transformed to obtain separated signals. Notably, an artifact mask is created by inverting the sum of all known signal masks, enabling WAND to capture and remove even unpredictable artifacts. The effectiveness of WAND in achieving accurate decomposition is demonstrated through numerical evaluations using simulated spectra. Furthermore, WAND's artifact removal capabilities significantly enhance the quantification accuracy of linear combination model fitting. The method's robustness is further validated using data from the 2016 MRS Fitting Challenge and in-vivo experiments.

A Deep Learning Approach Utilizing Covariance Matrix Analysis for the ISBI Edited MRS Reconstruction Challenge

This work proposes a method to accelerate the acquisition of high-quality edited magnetic resonance spectroscopy (MRS) scans using machine learning models taking the sample covariance matrix as input. The method is invariant to the number of transients and robust to noisy input data for both synthetic as well as in-vivo scenarios.