Diffusion magnetic resonance imaging is a noninvasive technique that is sensitive to the motion of water molecules in human tissue. The image signal is commonly described in q-space; however, a complete coverage of this space is often infeasible due to hardware and acquisition time limitations. In this work, we propose to represent the entire diffusion signal using an implicit neural representation network with wavelet activation functions. The signal space is encoded using Fourier features and spherical harmonics basis functions for a continuous output distribution of the raw diffusion data, enabling both super-resolution and q-space interpolation. Additionally, we introduce a pretraining strategy using a group template, enabling faster per-subject optimisation when combined with nonlinear registrations of subjects into template space. We tested the method with 10 subjects from the Human Connectome Project and 26 subjects from in-house data (multidimensional diffusion MRI from a Parkinson's disease cohort). The results show that the proposed method yields high-fidelity reconstructions with significantly reduced memory requirements compared to raw diffusion-weighted images. The pretraining scheme showed good generalisability properties on data acquired with very different protocols. We further assess the method on downstream metrics relevant to diffusion MRI data from the learned representations.
Figures & tables
Figure 1: Overview of the proposed representation for learning the DWI signal using an implicit neural representation (INR). The multi-shell DWI is represented as pairs of signal-space coordinates and corresponding scalar amplitude values. The spherical q-space signal-space coordinates are encoded via spherical harmonics function evaluations (bottom, centre).
Figure 2: a) First, the DWI signal, defined at multi-shell gradient directions, is transformed into the spherical harmonics domain by performing a linear least squares fit of the harmonic coefficients per shell. b) Then, individual shells in spherical harmonics form are affine-transformed and subsequently nonlinearly warped to MNI152 space. The affine and nonlinear deformations were obtained from the official HCP preprocessing pipeline [ 36 ] . c) Next, the spherical harmonics coefficients are averaged across all 50 subjects. d) Finally, a DWI template in spatial form is reconstructed by sampling the spherical harmonics representation at discrete gradient directions.
Method
MSE (×10−4)↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
LPIPS ↓
Leaky
2.52
0.0113
7.05
32.37
0.972
0.0164
SIREN
1.81
0.0100
7.35
33.75
0.978
0.0120
Wire
0.73
0.0063
4.43
37.74
0.991
0.0041
Table 1: Overall reconstruction performance (averaged across all voxels and shells) for the DWI template. Lower is better for MSE/MAE/RE/LPIPS, higher is better for PSNR/SSIM.
Training setup
MSE ( ×10−4 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
Unregistered
0.82±0.18
0.0065±0.00078
20.43±0.39
29.25±0.64
0.989±0.002
Pretrained Unreg.
0.92±0.21
0.0069±0.00080
21.56±0.31
27.09±0.58
0.844±0.009
Registered
0.40±0.05
0.0047±0.00029
5.30±1.15
35.46±0.65
0.989±0.001
Pretrained Reg.
0.70±0.07
0.0059±0.00037
6.10±1.26
33.49±0.56
0.986±0.001
Table 2: Overall reconstruction performance (mean ± std, averaged across all voxels and shells) on HCP subjects. Training time for the pretrained setups is a factor of 1/4 compared to the not pretrained ones.
Training setup
MSE ( ×10−4 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
Unregistered
5.80±0.15
0.0146±0.0018
15.88±3.92
26.39±1.17
0.972±0.005
Pretrained Unreg.
10.42±1.73
0.0195±0.0018
22.22±6.16
24.13±1.46
0.950±0.008
Registered
1.77±0.26
0.0092±0.0007
7.52±1.07
29.42±0.51
0.972±0.003
Pretrained Reg.
2.37±0.33
0.0103±0.0008
7.95±1.23
27.97±0.59
0.963±0.004
Table 3: Overall reconstruction performance (mean ± std across subjects, averaged across all voxels and shells) for 26 subjects from the ParkMR Dataset.
Training setup
b-value
Metric
MSE ( ×10−4 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
Unregistered
0
1.70±0.37
0.0095±0.0011
17.94±2.01
37.28±0.95
0.991±0.001
1000
0.64±0.16
0.0062±0.00080
16.11±0.42
28.15±0.85
0.987±0.002
2000
0.52±0.14
0.0056±0.00074
22.09±0.55
25.85±0.91
0.988±0.002
3000
0.41±0.11
0.0049±0.00068
25.52±0.38
25.71±0.95
0.990±0.002
Pretrained Unreg.
0
1.89±0.42
0.0100±0.0011
20.74±2.38
26.30±0.96
0.919±0.012
Table 4: Reconstruction quality per b-value for the four training setups (mean ± std across subjects) for the HCP data.
Figure 3: Relative error (mean ± std) of the Wire model when trained with 10-70% of diffusion directions for the registered HCP data with 288 gradient directions in total.
% of training
MSE ( ×10−4 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
10%
3.63 ± 0.70
0.0125 ± 0.0013
12.6 ± 2.6
26.7 ± 0.5
0.950 ± 0.006
30%
1.17 ± 0.13
0.0074 ± 0.0004
7.7 ± 1.6
31.4 ± 0.6
0.978 ± 0.001
50%
0.74 ± 0.14
0.0062 ± 0.0006
6.5 ± 1.4
33.1 ± 0.7
0.984 ± 0.002
70%
0.60 ± 0.10
0.0056 ± 0.0005
6.0 ± 1.2
33.8 ± 0.5
0.986 ± 0.002
Table 5: Overall reconstruction quality on the HCP subset for the Wire model with varying fractions of gradient directions used for training (mean ± std across subjects)
Figure 4: Visualisation of predicted and ground truth B0, MD and FA for a HCP subject.
Training setup
Parameter
Metric
MSE
MAE
Mean RE (%)
(25th RE, 75th RE) %
Unregistered
MD
0.000±0.0000
0.000061±0.000005
7.35±0.45
( 2.56,10.31 )
FA (WM)
0.027±0.0039
0.1371±0.0110
34.41±2.82
( 17.14,50.25 )
Pretrained Unreg
MD
0.000±0.0000
0.000069±0.000006
8.50±0.50
( 2.92,12.00 )
FA (WM)
0.039±0.0054
0.1678±0.0131
41.74±3.23
( 23.63,59.50 )
Registered
MD
0.000±0.0000
0.000021±0.000006
4.37±0.77
( 1.55,6.07 )
Table 6: Reconstruction quality for MD and FA (WM) parameters for the four training variants (mean ± std for MSE, MAE, Mean RE; mean for percentile RE) for the HCP subset.
Appendix figures & tables17 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: Signal flow diagram of the ParkMR nonlinear registration pipeline, exported from Nipype. The pipeline include the following stages: (1) general DWI preprocessing using MRtrix3; (2.a) nonlinear registration of T1 images to MNI 2 mm space using ANTs with affine and SyN transformations; (2.b) rigid registration of the mean b0 volume to the T1 image; (3) conversion of shell-specific DWI amplitudes to spherical harmonics (SH) with lmax=8 ; (4) spatial transformation of SH volumes using MRtrix3 with FOD reorientation; and (5) projection of SH signals onto a predefined, shell-specific gradient scheme, including duplication of the b0 image. Nodes use MRtrix3, ANTs, and utility functions within Nipype.
Subject Info
Controls
PD Patients
Mean age ± SD [min–max]
60±6[50–78]
63±9[47–78]
Gender [F:M]
3:14
3:9
Disease duration [years]
–
6.4±5.3[1–17]
LEDD [mg]
–
479±301[72–958]
H & Y stage
–
1.75±0.45[1–2]
MoCA
–
28.9±1.2[27–30]
Appendix
Table 7: Demographic and clinical characteristics of the study cohort for the MD-dMRI data. Values are reported as mean ± SD with the range in square brackets. A dash (–) indicates “not applicable”.
Training setup
b-value
Metric
MSE ( ×10−4 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
Unregistered
0
19.84±5.30
0.0317±0.0041
19.13±3.42
27.04±1.15
0.9546±0.0076
100
5.55±1.52
0.0164±0.0022
11.69±2.33
30.06±0.81
0.9778±0.0035
700
1.51±0.39
0.0094±0.0012
13.38±3.51
25.47±1.89
0.9733±0.0054
1400
1.14±0.32
0.0081±0.0012
16.92±5.24
24.58±1.98
0.9761±0.0060
2000
0.95±0.28
0.0073±0.0011
18.27±6.13
24.78±2.11
0.9786±0.0060
Appendix
Table 8: Quantitative metrics (mean ± std across subjects) for the ParkMR data. Lower is better for MSE/MAE/RE, higher is better for PSNR/SSIM.
Method
b-value
Metric
MSE (×10−4)↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
Leaky
0
2.24
0.0108
7.18
36.50
0.980
1000
4.07
0.0148
6.51
31.57
0.969
2000
2.22
0.0108
7.08
30.75
0.968
3000
1.58
0.0088
7.41
30.63
0.970
Siren
0
1.09
0.0079
6.86
39.63
0.990
Appendix
Table 9: Reconstruction quality per b-value for the Leaky , Siren and Wire models on the DWI template. Lower is better for MSE/MAE/RE, higher is better for PSNR/SSIM.
Figure 6: Fibre Orientation Distributions (FODs) from a coronal slice of the group-averaged DWI template. Ground truth FODs (top) and predictions from the Wire model (bottom) are shown.
Figure 7: Native space. Qualitative comparison in native DWI space (no template registration). Four columns correspond to the target shells ( b=0 , 1000 , 2000 , 3000 s/mm 2 ); within each column, the top pair shows the INR prediction ( Pred ) and the bottom pair the acquired ground truth ( GT ). Rows 1–2: INR trained from scratch in native space ( Unregistered ). Rows 3–4: template-initialised INR fitted in native space ( Pretrained – Reg ). Template pretraining reduces training time to one-quarter.
Figure 8: Registered space. Same layout as Fig. 7 , but after rigid registration to the b=0 volume. Rows 1–2: INR trained from scratch in registered space ( Registered ). Rows 3–4: template-initialised INR ( Pretrained + Reg ) with 1/4 of training time.
Parameter Category
Hyperparameter
Value
Optimization
Learning Rate ( lr )
varied
Cosine LR Scheduler ( use_cos_lrsheduler )
True
Training Batch Size ( train_batch_size )
262,144
Epochs ( epochs )
varied
Model Architecture
Network Type ( network_name )
varied
Input Dimensionality ( in_size )
301
Appendix
Table 10: Key hyperparameters for the model training and architecture. Variable names from the configuration are shown in monospace . The parameters that differ across the experiments are indicated by: varied .
Model Type
Parameter
Value
Siren
First Layer ω0
30.0
Hidden Layer ωh
30.0
Wire
ω
10.0
σ
40.0
Shared Encoders
Fourier Encoder Frequencies
128
Fourier Feature Dim.
256
Appendix
Table 11: Model-specific parameters for Wire , Siren models and feature encoding methods.
Parameter Category
Hyperparameter
Value
Optimization
Learning Rate ( lr )
0.001
Cosine LR Scheduler ( use_cos_lrsheduler )
True
Training Batch Size ( train_batch_size )
262,144
Epochs ( epochs )
64
Model Architecture
Network Type ( network_name )
Leaky ReLU, Siren , Wire
Input Dimensionality ( in_size )
301
Appendix
Table 12: Hyperparameters for training the INR on the group-averaged DWI template.
Parameter Category
Hyperparameter
Value
Optimization
Learning Rate ( lr )
0.0001
Cosine LR Scheduler ( use_cos_lrsheduler )
True
Training Batch Size ( train_batch_size )
262,144
Epochs ( epochs )
Baseline: 64, Pretrained: 16
Model Architecture
Network Type ( network_name )
Wire
Input Dimensionality ( in_size )
301
Appendix
Table 13: Hyperparameters for pretraining and registration experiments.
Parameter Category
Hyperparameter
Value
Optimization
Learning Rate ( lr )
0.001
Cosine LR Scheduler ( use_cos_lrsheduler )
True
Training Batch Size ( train_batch_size )
262,144
Epochs ( epochs )
16
Model Architecture
Network Type ( network_name )
Wire (from checkpoint)
Input Dimensionality ( in_size )
301
Appendix
Table 14: Key hyperparameters for the b-vector interpolation experiments.
Parameter Category
Hyperparameter
Value
Optimization
Learning Rate ( lr )
0.001
Cosine LR Scheduler ( use_cos_lrsheduler )
True
Training Batch Size ( train_batch_size )
262,144
Epochs ( epochs )
32
L2-regularisation strength
0.0001
b-value dropout
0.5
Appendix
Table 15: Key hyperparameters for the b-value interpolation experiments.
Figure 9: Relative error (mean ± std) of the SHORE model when fitted to 10–70% of diffusion directions for the registered HCP data with 288 gradient directions in total. Data and setup correspond to the main paper, Figure 3.
Parameter Category
Hyperparameter
Value
Optimization
Learning Rate ( lr )
0.001
Cosine LR Scheduler ( use_cos_lrsheduler )
True
Training Batch Size ( train_batch_size )
262,144
Epochs ( epochs )
32
Model Architecture
Network Type ( network_name )
Wire (from checkpoint)
Input Dimensionality ( in_size )
301
Appendix
Table 16: Hyperparameters used for superresolution experiments.
Upscaling factor
b-value
Metric
MSE ( ×10−3 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
4×
0
6.67±1.57
0.051±0.010
28.8±4.0
21.9±1.0
0.794±0.019
1000
1.30±0.68
0.027±0.008
28.3±6.0
20.8±1.4
0.858±0.028
2000
0.829±0.772
0.023±0.011
28.9±10.0
19.6±2.5
0.896±0.038
3000
0.731±0.823
0.022±0.012
30.5±12.3
18.9±3.2
0.911±0.046
2×
0
4.17±1.17
0.039±0.010
20.4±3.7
24.0±1.2
0.879±0.009
Appendix
Table 17: Reconstruction quality per b-value (mean ± std across subjects) for 4× and 2× superresolution on the HCP data.
Upscaling factor
MSE ( ×10−3 ) ↓
MAE ↓
RE (%) ↓
PSNR (dB) ↑
SSIM ↑
4×
2.383±0.785
0.031±0.009
29.1±6.9
20.3±1.7
0.865±0.031
2×
1.372±0.472
0.022±0.007
19.9±5.1
23.4±1.7
0.930±0.014
No upscaling
0.40±0.05
0.0047±0.00029
5.30±1.15
35.46±0.65
0.989±0.001
Appendix
Table 18: Overall reconstruction performance (mean ± std, averaged across all voxels and shells) for the two upscaling factors.
Resolving complex fiber geometries in brain white matter requires high-resolution diffusion MRI at the cost of long acquisition times. This leads many clinical protocols to opt for low-resolution scans, making downstream microstructure estimation and tractography challenging. Implicit neural representations (INRs) can model the diffusion signal continuously, enabling native single-subject super-resolution by querying the network at arbitrary spatial coordinates, yet existing methods often suffer from long training times and lack a mechanism to incorporate anatomical priors to regularize super-resolution by constraining the space of plausible reconstructions. To address these limitations, we propose a novel transfer-learning framework that pre-trains an INR on a high-resolution template and then adapts it to subject-specific scans via registration and fine-tuning. For 4× through-plane super-resolution from 5 mm to 1.25 mm on Human Connectome Project (HCP) data, our method reduces NRMSE by 36-49% and increases FSIM by 24-43% over a recent baseline with 6× faster training, outperforming competing INR-based methods across both image quality and domain-specific metrics. Code is available on the project page at https://abdulkaderghandoura.github.io/research/msc-thesis/ .
Abdulkader Ghandoura, Marsil Zakour, William Consagra +1
Psychiatry Neuroimaging Laboratory Brigham and Women’s Hospital Harvard Medical School Boston, MA, USA · School of Computation, Information and Technology Technical University of Munich Munich, Germany · Department of Statistics University of South Carolina Columbia, SC, USA
Diffusion MRI (dMRI) probes water diffusion within the brain, providing unique information about tissue microstructure and white matter connectivity. High-quality dMRI enables advanced and accurate analyses but demands dense acquisitions, resulting in long scan times and hardware constraints that are often infeasible. Further, dMRI requires dedicated computational methods to support diverse analysis tasks (e.g., parcellation, registration, and synthesis) for both neuroscientific and clinical applications. Here, we present dMRI-F, a foundation model that unifies dMRI data enhancement and downstream tasks across diverse acquisitions and populations, while requiring only minimal acquisition input. dMRI-F is pre-trained with a q-space masked reconstruction task: predicting densely sampled multi-shell data from only six volumes. It learns generalizable latent feature representations of dMRI data, which serve as a core foundation for adapting to diverse downstream tasks, including brain parcellation, brain registration, and cross-modal synthesis. Across nine independently acquired datasets, we demonstrate that dMRI-F outperforms state-of-the-art methods with robust generalization across acquisitions, populations, and tasks. Our results demonstrate dMRI-F's versatility as a general-purpose framework that enables diverse dMRI applications from low-cost, sparse acquisitions.
Xi Zhu, Yijie Li, Xiaofan Wang +4
University of Electronic Science and Technology of China.
Diffusion Magnetic Resonance Imaging (dMRI) plays a critical role in studying microstructural changes in the brain. It is, therefore, widely used in clinical practice; yet progress in learning general-purpose representations from dMRI has been limited. A key challenge is that existing deep learning approaches are not well-suited to capture the unique properties of diffusion signals. Brain dMRI is normally composed of several brain volumes, each with different attenuation characteristics dependent on the direction and strength of the diffusion-sensitized gradients. Thus, there is a need to jointly model spatial, diffusion-weighting, and directional dependencies in dMRI. Furthermore, varying acquisition protocols (e.g., differing numbers of directions) further limit traditional models. To address these gaps, we introduce a diffusion space rotatory positional embedding (D-RoPE) plugged into our dMRI transformer to capture both the spatial structure and directional characteristics of diffusion data, enabling robust and transferable representations across diverse acquisition settings and an arbitrary number of diffusion directions. After self-supervised masked autoencoding pretraining, tests on several downstream tasks show that the learned representations and the pretrained model can provide competitive or superior performance compared to several baselines in these downstream tasks (even compared to a fully trained baseline); the finetuned features from our pretrained encoder resulted in a 6% higher accuracy in classifying mild cognitive impairment and a 0.05 increase in the correlation coefficient when predicting cognitive scores. Code is available at: github.com/gustavochau/D-RoPE.
Gustavo Chau Loo Kung, Mohammad Abbasi, Camila Blank +6