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

Mohamed Abouagour; Atharva Shah; Eleftherios Garyfallidis

cs.CVMar 31, 2026

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

Authors: Mohamed Abouagour, Atharva Shah, Eleftherios Garyfallidis

Organizations: Indiana University, Bloomington, IN, USA

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.

Figures & tables

Figure 1: PRISM analysis-by-synthesis pipeline. The multi-compartment tissue signal model $\mathcal{S}(\boldsymbol{\theta}_{\mathrm{micro}})$ (top, green) combines up to $K$ white-matter fiber populations with gray matter, CSF, and a restricted compartment. A nuisance calibration module $\mathcal{A}(\boldsymbol{\theta}_{\mathrm{cal}})$ (bottom, orange) applies a smooth bias field $B(\mathbf{x})$ , per-measurement affine correction $(\alpha_{n},\beta_{n})$ , and noise level $\sigma$ . The differentiable forward model synthesizes the expected measurement $\hat{y}{=}\mathcal{A}(\mathcal{S})$ , which is compared to observed multi-shell dMRI via an MSE or NLL loss plus regularization $\mathcal{R}(\boldsymbol{\theta})$ . Rprop updates tissue and calibration parameters jointly through gradient-based optimization.

Method	1-fib	$15^{\circ}$	$20^{\circ}$	$25^{\circ}$	$30^{\circ}$	$45^{\circ}$	$60^{\circ}$	$75^{\circ}$	$90^{\circ}$	Overall	F1	Rec.
PRISM MSE	0.7	7.5	9.9	11.7	8.2	1.9	1.5	1.5	1.3	3.5	96	95
PRISM NLL	1.4	5.8	4.9	3.9	3.1	1.9	1.5	1.3	1.3	2.3	99	99
CSD	3.1	7.9	10.3	12.7	15.2	8.8	3.9	4.0	3.5	7.7	90	82
MSMT-CSD	3.0	7.8	10.2	12.7	15.2	5.3	3.4	3.2	3.1	6.8	91	83
ODF-FP	3.1	7.4	9.7	11.9	13.7	16.9	10.9	9.4	10.9	11.6	87	86

Table 1: Best-match angular error (°) at SNR = 30 (16 angles, 15–90°; representative subset). F1 and recall (%) over all angles.

	Rprop	Adam	Adam (.05)	AdamW	NAdam	RMSprop	Adagrad	SGD+m
MSE ( $\!\times\!10^{-3}$ )	21.2	24.4	21.5	24.4	24.5	21.5	45.7	85.3
Iter $\to$ thr	22	$>$ 200	63	$>$ 200	$>$ 200	39	$>$ 200	$>$ 200

Table 2: Optimizer comparison (200 iterations, Stanford HARDI, 20 middle axial slices,

n{=}3

fibers, seed-42 init). Convergence threshold (Iter

\to

thr): iteration first reaching 110% of best final MSE. Rprop achieves the lowest final MSE and converges fastest.

Diffusion MRI

Diffusion MRI measures water motion in tissue to characterize brain microstructure, white-matter pathways, and disease.

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Fiber-Resolved Microstructure Quantification from Multi-Shell Diffusion MRI using Detection Transformers

Sebastian Endt, Marcus Wirth, Johannes Reinhold Schlund, Marion Irene Menzel

AImotion Bavaria, Technische Hochschule Ingolstadt, Ingolstadt, Germany · TUM School of Computation, Information and Technology, Technical University of Munich, Garching, Germany · TUM School of Natural Sciences, Technical University of Munich, Garching, Germany

Diffusion MRI

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Fiber orientation and compartmental microstructure are central to the characterization of white matter tissue in diffusion MRI, yet existing methods either resolve fiber orientations without quantifying microstructure, or quantify microstructure while assuming a fixed number of compartments and a single fiber direction. Nonparametric approaches that recover both require tensor-valued diffusion encoding and computationally expensive Monte-Carlo inversion of an ill-posed inverse Laplace transform. We propose to reframe this problem as an object detection-like task, adopting the Detection Transformer (DETR) architecture to jointly predict mean diffusivity (MD), fractional anisotropy (FA), main fiber direction, and signal fraction for a variable number of compartments per voxel from standard multi-shell diffusion MRI with linear encoding. Hungarian matching during training resolves permutation invariance across compartments. We introduce mean Average Precision as a reproducible benchmark metric. Evaluated on synthetic test data with up to five compartments per voxel, our model achieves

R^2=0.95

for MD,

R^2=0.88

for FA, and a median angular error of 4.2°, with performance scaling naturally with compartmental signal fraction.

Abstract

Diffusion MRI

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