Neural Orientation Distribution Fields for Estimation and Uncertainty Quantification in Diffusion MRI

TL;DR

This paper introduces a deep learning approach using neural fields for continuous estimation and uncertainty quantification of orientation distribution functions in diffusion MRI, improving accuracy in noisy and sparse data conditions.

Contribution

A novel neural field-based method for continuous ODF estimation that models spatial correlations and provides efficient uncertainty quantification without resampling.

Findings

Outperforms existing methods on synthetic data

Accurately estimates ODFs in real in-vivo diffusion MRI

Provides reliable uncertainty measures at each spatial location

Abstract

Inferring brain connectivity and structure \textit{in-vivo} requires accurate estimation of the orientation distribution function (ODF), which encodes key local tissue properties. However, estimating the ODF from diffusion MRI (dMRI) signals is a challenging inverse problem due to obstacles such as significant noise, high-dimensional parameter spaces, and sparse angular measurements. In this paper, we address these challenges by proposing a novel deep-learning based methodology for continuous estimation and uncertainty quantification of the spatially varying ODF field. We use a neural field (NF) to parameterize a random series representation of the latent ODFs, implicitly modeling the often ignored but valuable spatial correlation structures in the data, and thereby improving efficiency in sparse and noisy regimes. An analytic approximation to the posterior predictive distribution is derived which can be used to quantify the uncertainty in the ODF estimate at any spatial location, avoiding the need for expensive resampling-based approaches that are typically employed for this purpose. We present empirical evaluations on both synthetic and real in-vivo diffusion data, demonstrating the advantages of our method over existing approaches.