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Inferring brain connectivity and structure \textit{in-vivo} requires accurateestimation of the orientation distribution function (ODF), which encodes keylocal tissue properties. However, estimating the ODF from diffusion MRI (dMRI)signals is a challenging inverse problem due to obstacles such as significantnoise, high-dimensional parameter spaces, and sparse angular measurements. Inthis paper, we address these challenges by proposing a novel deep-learningbased methodology for continuous estimation and uncertainty quantification ofthe spatially varying ODF field. We use a neural field (NF) to parameterize arandom series representation of the latent ODFs, implicitly modeling the oftenignored but valuable spatial correlation structures in the data, and therebyimproving efficiency in sparse and noisy regimes. An analytic approximation tothe posterior predictive distribution is derived which can be used to quantifythe uncertainty in the ODF estimate at any spatial location, avoiding the needfor expensive resampling-based approaches that are typically employed for thispurpose. We present empirical evaluations on both synthetic and real in-vivodiffusion data, demonstrating the advantages of our method over existingapproaches.

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