MaxEnt-DTD: Maximum-Entropy Estimation of Diffusion Tensor Distribution for Fiber Orientation and Microstructure Characterization

Diffusion MRI (dMRI) enables noninvasive characterization of white-matter fiber orientations and tissue microstructure, but widely used approaches, such as constrained spherical deconvolution (CSD) and parametric multicompartment models, typically address these features separately. The diffusion tensor distribution (DTD) framework jointly represents fiber orientation and microstructure, but estimating DTD from finite, noisy measurements is severely ill-posed. Existing inversion methods either rely on nonnegativity constrained basis representations, which are challenging to sale to high-dimensional and high-resolution distributions, or use sampling-based approaches with limited reliability. We propose MaxEnt-DTD, a maximum-entropy algorithm for DTD estimation from finite and noisy dMRI data. By deriving the Lagrange dual formulation, we reformulate a constrained infinite-dimensional optimization problem into a finite-dimensional unconstrained convex optimization problem, substantially reducing the parameter space and enabling tractable whole-brain DTD estimation. We evaluate MaxEnt-DTD using both synthetic and in vivo data from the Human Connectome Project protocol and a second dataset using advanced B-tensor diffusion encoding. We compare MaxEnt-DTD-derived fiber orientation distributions with results from CSD and Monte-Carlo inversion methods, and assess fiber-specific microstructure measures and rotation-invariant metrics based on the cumulants of DTD. The results demonstrate that MaxEnt-DTD provides a reliable and efficient framework for joint fiber-orientation and microstructure analysis in dMRI.