PRISM: Differentiable Analysis-by-Synthesis for Fixel Recovery in Diffusion MRI

2026-03-31

AI Summary

This work addresses the challenge of accurately recovering small-angle crossing fibers in diffusion MRI, where conventional voxel-wise fitting often fails. The authors propose PRISM, a novel framework that introduces, for the first time, an end-to-end differentiable analysis–synthesis strategy into microstructural modeling. PRISM jointly optimizes an explicit multi-compartment forward model—comprising CSF, gray matter, multiple white matter fascicles, and a restricted compartment—with fiber orientations over image patches. Soft model selection is achieved through repulsive and sparsity priors, and the method enables Rician likelihood learning without requiring explicit noise priors. Experiments demonstrate that PRISM achieves a 2.3° angular error with 99% recall on synthetic data, resolving crossings as acute as 20°, attains a connectivity correlation of 0.934 on the DiSCo1 phantom, and fits whole-brain Human Connectome Project (HCP) data in approximately 12 minutes.

Abstract

Diffusion MRI microstructure fitting is nonconvex and often performed voxelwise, which limits fiber peak recovery in narrow crossings. This work introduces PRISM, a differentiable analysis-by-synthesis framework that fits an explicit multi-compartment forward model end-to-end over spatial patches. The model combines cerebrospinal fluid (CSF), gray matter, up to K white-matter fiber compartments (stick-and-zeppelin), and a restricted compartment, with explicit fiber directions and soft model selection via repulsion and sparsity priors. PRISM supports a fast MSE objective and a Rician negative log-likelihood (NLL) that jointly learns sigma without oracle information. A lightweight nuisance calibration module (smooth bias field and per-measurement scale/offset) is included for robustness and regularized to identity in clean-data tests. On synthetic crossing-fiber data (SNR=30; five methods, 16 crossing angles), PRISM achieves 3.5 degrees best-match angular error with 95% recall, which is 1.9x lower than the best baseline (MSMT-CSD, 6.8 degrees, 83% recall); in NLL mode with learned sigma, error drops to 2.3 degrees with 99% recall, resolving crossings down to 20 degrees. On the DiSCo1 phantom (NLL mode), PRISM improves connectivity correlation over CSD baselines at all four tracking angles (best r=.934 at 25 degrees vs. .920 for MSMT-CSD). Whole-brain HCP fitting (~741k voxels, MSE mode) completes in ~12 min on a single GPU with near-identical results across random seeds.

Problem

• diffusion MRI
• microstructure fitting
• fiber crossing
• nonconvex optimization
• fixel recovery

Innovation

• differentiable analysis-by-synthesis
• multi-compartment modeling
• fiber orientation estimation
• Rician noise learning
• spatial patch fitting