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.

翻译：推断活体大脑的连通性与结构需要准确估计取向分布函数（ODF），该函数编码了关键的局部组织特性。然而，由于显著噪声、高维参数空间以及稀疏角度测量等障碍，从扩散磁共振成像（dMRI）信号中估计ODF是一项具有挑战性的逆问题。本文提出了一种基于深度学习的新型方法，用于实现空间变化ODF场的连续估计与不确定度量化。我们利用神经场（NF）参数化潜在ODF的随机级数表示，隐式建模了数据中常被忽略但宝贵的空间相关结构，从而提升了稀疏与噪声条件下的效率。推导了后验预测分布的解析近似，该近似可用于量化任意空间位置ODF估计的不确定度，避免了通常为此采用的昂贵重采样方法。我们在合成数据与真实活体扩散数据上进行了实证评估，证明了本方法相对于现有方法的优势。