DTI-Guided Volumetric Spherical Harmonics Regression for Single-to-Multi-Shell dMRI Synthesis

Binghua Li; Christina Andica; Tong Liang; Ziqing Chang; Chao Li; Wataru Uchida; Kaito Takabayashi; Qibin Zhao

cs.CVSep 13, 2026

DTI-Guided Volumetric Spherical Harmonics Regression for Single-to-Multi-Shell dMRI Synthesis

Authors: Binghua Li, Christina Andica, Tong Liang, Ziqing Chang, Chao Li, Wataru Uchida, Kaito Takabayashi, Qibin Zhao,

Organizations: Juntendo University, Tokyo, Japan · RIKEN Center for Advanced Intelligence Project, Tokyo, Japan · Tokyo University of Agriculture and Technology, Tokyo, Japan

Abstract

Multi-shell diffusion MRI (dMRI) unlocks more expressive microstructural modeling than single-shell scans, yet its longer acquisition time hinders deployment in large-scale cohorts and time-constrained clinical settings. Synthesizing an unobserved shell from a single-shell input is fundamentally ill-posed and further complicated by protocol mismatch, where source and target gradient direction sets may not align. We propose DTI-SHNet, a single-to-multi-shell synthesis framework that operates in the real symmetric spherical harmonics (SH) coefficient domain and performs spatially aware volumetric regression. Given a source shell, we estimate diffusion tensor imaging (DTI) and use direction-agnostic parametric maps along with a brain mask as conditioning priors to guide a 3D U-Net regressor from source-shell to target-shell SH coefficients. To couple coefficient accuracy with signal fidelity, we introduce a signal consistency regularization that reconstructs signals on randomly sampled canonical directions from predicted coefficients and enforces agreement in the signal domain. Experiments on UK Biobank and Cam-CAN data for b=1000 to b=2000 dMRI synthesis show that DTI-SHNet achieves competitive visual quality compared to advanced methods, while better preserving downstream diffusion measures. Our code is available at https://github.com/xiaovhua/dti-shnet.

Figures & tables

Figure 1: Overview of our synthesis pipeline. Single-shell data at $b=b_{1}$ are represented as real symmetric SH coefficient volumes $C_{b_{1}}$ . DTI-SHNet predicts target coefficient volumes $\widehat{C}_{b_{2}}$ guided by DTI priors. Target-shell signals are synthesized for desired directions by SH reconstruction, with an additional signal consistency constraint $\mathcal{L}_{\mathrm{sig}}$ applied on canonical directions sampled during training.

Figure 2: Framework of DTI-SHNet. A 3D U-Net regresses target-shell SH coefficients from source-shell coefficients, conditioned on DTI priors.

Figure 3: Qualitative comparison for $b{=}2000$ synthesis from $b{=}1000$ on Cam-CAN. Representative slices illustrate that DTI-SHNet better preserves anatomical structures and reduces artifacts compared with competing baselines.

Method	UKB			Cam-CAN
Method	PSNR $\uparrow$	SSIM $\uparrow$	NMSE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	NMSE $\downarrow$
Extrapolation [ 2 ]	$21.9\pm 0.6$	$0.825\pm 0.014$	$0.180\pm 0.028$	$22.0\pm 0.5$	$0.805\pm 0.014$	$0.134\pm 0.023$
DDPM [ 5 ]	$21.5\pm 0.8$	$0.824\pm 0.022$	$0.229\pm 0.030$	$24.0\pm 0.8$	$0.883\pm 0.023$	$0.109\pm 0.021$
SH-DNN [ 11 ]	$25.6\pm 0.7$	$0.930\pm 0.007$	$0.079\pm 0.016$	$26.7\pm 0.5$	$0.951\pm 0.005$	$0.045\pm 0.007$
DirUNet [ 4 ]	$24.1\pm 0.6$	$0.895\pm 0.010$	$0.109\pm 0.022$	$29.0\pm 0.6$	$0.968\pm 0.004$	$0.026\pm 0.004$
DTI-SHNet	$25.3\pm 0.7$	$0.922\pm 0.008$	$0.083\pm 0.018$	$29.3\pm 0.6$	$0.970\pm 0.004$	$0.025\pm 0.004$

Table 1: Main results on UKB and Cam-CAN for synthesizing

b{=}2000

from

b{=}1000

Condition		UKB					Cam-CAN
Priors	$\mathcal{L}_{\mathrm{sig}}$	PSNR $\uparrow$	SSIM $\uparrow$	NMSE $\downarrow$	$\Delta$ FA $\downarrow$	$\Delta$ MD $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	NMSE $\downarrow$	$\Delta$ FA $\downarrow$	$\Delta$ MD $\downarrow$
$\times$	$\times$	25.33	0.9218	0.0829	0.0235	0.337	27.90	0.9547	0.0341	0.0604	0.903
$\checkmark$	$\times$	25.42	0.9235	0.0814	0.0224	0.322	28.64	0.9627	0.0288	0.0418	0.656
$\times$	$\checkmark$	25.29	0.9219	0.0838	0.0233	0.282	28.61	0.9639	0.0290	0.0343	0.467
$\checkmark$	$\checkmark$	25.33	0.9216	0.0830	0.0220	0.281	29.32	0.9700	0.0246	0.0319	0.426

Table 3: Ablation study on the DTI-derived priors and the signal consistency loss

\mathcal{L}_{\mathrm{sig}}

for synthesizing

b{=}2000

from

b{=}1000

\Delta\mathrm{MD}

is scaled by

10^{-4}

Figure 4: Qualitative NODDI comparison between ground-truth multi-shell dMRI and synthesized multi-shell dMRI. We show representative maps of the NDI, ODI, and ISO, together with their corresponding histograms.

Medical Image Synthesis

Medical image synthesis creates, translates, reconstructs, and edits clinical images to fill missing data and support analysis.

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WFM: 3D Wavelet Flow Matching for Ultrafast Multi-Modal MRI Synthesis

Yalcin Tur, Mihajlo Stojkovic, Ulas Bagci

Department of Computer Science, Stanford University, Stanford, CA, USA · Machine and Hybrid Intelligence Lab, Feinberg School of Medicine, Northwestern University, Chicago, IL, USA

Flow Matching BraTS Magnetic Resonance Imaging Medical Image Synthesis

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Diffusion models have achieved remarkable quality in multi-modal MRI synthesis, but their computational cost (hundreds of sampling steps and separate models per modality) limits clinical deployment. We observe that this inefficiency stems from an unnecessary starting point: diffusion begins from pure noise, discarding the structural information already present in available MRI sequences. We propose WFM (Wavelet Flow Matching), which instead learns a direct flow from an informed prior, the mean of conditioning modalities in wavelet space, to the target distribution. Because the source and target share underlying anatomy and differ primarily in contrast, this formulation enables accurate synthesis in just 1-2 integration steps. A single 82M-parameter model with class conditioning synthesizes all four BraTS modalities (T1, T1c, T2, FLAIR), replacing four separate diffusion models totaling 326M parameters. On BraTS 2024, WFM achieves 26.8 dB PSNR and 0.94 SSIM, within 1-2 dB of diffusion baselines, while running 250-1000x faster (0.16-0.64s vs. 160s per volume). This speed-quality trade-off makes real-time MRI synthesis practical for clinical workflows. Code is available at https://github.com/yalcintur/WFM.

Abstract

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