PaDIS-MRI: Patch-Based Diffusion MRI Reconstruction

• PaDIS-MRI is a diffusion-based MRI reconstruction method that uses a learned patch prior and positional encoding to recover images from undersampled k-space data.
• It employs a complex-valued representation and patch-based denoising combined with diffusion posterior sampling to maintain data consistency and preserve fine anatomical details.
• The approach demonstrates superior data efficiency in low-data regimes compared to whole-image diffusion models, leading to enhanced PSNR, SSIM, and radiologist preference.

PaDIS-MRI is a diffusion-based MRI reconstruction method for data-scarce accelerated MRI. It extends the Patch-based Diffusion Inverse Solver (PaDIS) to complex-valued, multi-coil MRI reconstruction, with the central premise that a patch-based diffusion prior can be more data-efficient than a whole-image diffusion prior when reconstructing anatomical images from undersampled k-space measurements. In the formulation described by the method, reconstruction is performed from undersampled multi-coil k-space data using a learned local prior, positional encoding, and diffusion posterior sampling, rather than a full-image generative prior trained on large fully sampled datasets (Sanda et al., 25 Sep 2025, Hu et al., 2024).

1. Conceptual basis and problem setting

PaDIS-MRI addresses accelerated MRI, where acquisition time is reduced by undersampling k-space. In the setting considered by the method, reconstruction seeks an anatomical image $x$ from undersampled multi-coil measurements $y$, so the inverse problem is ill-posed and requires a strong prior over plausible MR images. The method is explicitly motivated by clinical regimes in which fully sampled training data are scarce and where standard whole-image diffusion priors are poorly matched to small-data conditions, because they must model complete MR images, global anatomy, and contrast-specific structure from limited examples (Sanda et al., 25 Sep 2025).

The MRI forward model is written as

$y = P F S x + \epsilon,$

where $x \in \mathbb{C}^{N_x N_y}$ is the vectorized complex image, $S$ is the coil sensitivity operator, $F$ is the Fourier transform operator, $P$ is the undersampling operator, and $\epsilon$ is complex-valued additive noise. The forward operator is defined as $\mathcal{A}=PFS$, and the reconstruction objective is written as

$$\tilde{x} = \arg\min_x \|y - \mathcal{A}x\|_2^2 + \lambda \mathcal{R}(x),$$

with the corresponding Bayesian form

$y$0

The defining claim of PaDIS-MRI is that local anatomical structure is more reusable and statistically easier to learn than whole-image structure. Small training sets can still provide many patches containing edges, tissue interfaces, ventricles, and gyri patterns. This suggests that, under constrained sample budgets, a patch prior can reduce the sample complexity of learning a useful MRI prior while preserving compatibility with posterior sampling.

2. Patch-based diffusion prior and complex-valued formulation

The method’s core departure from whole-image diffusion reconstruction is the substitution of a patch prior for a global full-image prior. PaDIS-MRI inherits from PaDIS the idea that the global score can be assembled from local patch scores. The identity reproduced in the method description is

$y$1

where $y$2 indexes patch-grid offsets, $y$3 is a patch in that partition, and $y$4 is its score (Sanda et al., 25 Sep 2025).

Because evaluating all offset partitions is expensive, one random partition is sampled per diffusion iteration. Over many iterations, this Monte Carlo averaging is used to reduce patch-boundary artifacts. Position information is preserved through a 2D positional encoding that provides each patch with its absolute $y$5 location normalized to $y$6. The denoiser is therefore not purely local in the sense of texture modeling alone; it is location-aware, which allows the prior to distinguish anatomically plausible local structures by spatial context.

A further technical distinction is the treatment of MRI as complex-valued data. PaDIS-MRI represents each complex patch as a 2-channel real tensor, with one channel for the real part and one channel for the imaginary part. The same representation is used during training and inference, after which the two real channels are converted back into a complex patch or image. This complex-valued representation is one of the principal extensions beyond the original PaDIS framework, which was introduced as a patch-based position-aware diffusion inverse solver for inverse problems more broadly rather than specifically for complex-valued multi-coil MRI (Hu et al., 2024).

3. Diffusion posterior sampling and reconstruction procedure

PaDIS-MRI uses score-based diffusion and Diffusion Posterior Sampling (DPS). The forward SDE is written as

$y$7

and the reverse-time SDE as

$y$8

For inverse problems, DPS augments the reverse process with a data-consistency gradient,

$y$9

with

$y = P F S x + \epsilon,$0

The method uses the VE discretization of EDM with noise schedule

$y = P F S x + \epsilon,$1

and defines

$y = P F S x + \epsilon,$2

The data consistency weight is reported as $y = P F S x + \epsilon,$3 (Sanda et al., 25 Sep 2025).

The practical inference procedure starts from the adjoint reconstruction $y = P F S x + \epsilon,$4, pads the image, injects VE noise at each diffusion step, randomly chooses a patch-grid offset, extracts non-overlapping $y = P F S x + \epsilon,$5 patches, converts each complex patch into two real channels, denoises all patches with the patch model and positional encodings, reassembles the denoised patches into a full padded image, forms the score estimate, crops back to the original field of view to evaluate the MRI forward model, computes the residual $y = P F S x + \epsilon,$6, and backpropagates through the forward operator to obtain $y = P F S x + \epsilon,$7. The sampler uses $y = P F S x + \epsilon,$8 noise levels, 10 inner update iterations per level, and 1040 network calls, with fixed inference patch size $y = P F S x + \epsilon,$9 and zero-padding $x \in \mathbb{C}^{N_x N_y}$0 pixels on each side.

A common misconception is that PaDIS-MRI is simply a patchwise denoiser pasted onto MRI reconstruction. The reconstruction loop is instead a posterior-guided iterative sampler in which patch denoising, positional encoding, and measurement consistency are jointly coupled through the MRI forward model.

4. Training regime, architecture, and data efficiency

The experiments use the public FastMRI brain multicoil dataset from NYU Langone, including FLAIR, native T1, pre-contrast T1, post-contrast T1, and axial T2-weighted scans. The training set contains 446 k-space volumes, the validation pool 266 distinct volumes, and the evaluation set 82 center slices, consisting of 50 T2-axial, 7 FLAIR, and 25 T1-weighted images (Sanda et al., 25 Sep 2025).

The small-data study is organized around training-set sizes

$x \in \mathbb{C}^{N_x N_y}$1

where $x \in \mathbb{C}^{N_x N_y}$2 counts k-space slices. For 25, 100, and 200, only center slices are used; for 500, two adjacent slices from 250 volumes; for 1000, four adjacent slices from 250 volumes; and for 2330, five slices from each of 446 volumes. Preprocessing follows the FastMRI-EDM baseline: inverse Fourier transform to coil images, zero-padding to $x \in \mathbb{C}^{N_x N_y}$3, coil-noise covariance estimation from a $x \in \mathbb{C}^{N_x N_y}$4 background patch, pre-whitening using BART, normalization via a $x \in \mathbb{C}^{N_x N_y}$5 centered ACS reconstruction scaled by its 99th percentile, and retrospective Cartesian masks with a fully sampled $x \in \mathbb{C}^{N_x N_y}$6 ACS region.

The PaDIS-MRI denoiser is a Song-UNet-based network with about 55M parameters, 128 base channels, multipliers $x \in \mathbb{C}^{N_x N_y}$7, dropout 0.05, batch size 4, and Adam with learning rate $x \in \mathbb{C}^{N_x N_y}$8 and betas $x \in \mathbb{C}^{N_x N_y}$9. Training uses FP32. Patch sizes are randomized with

$S$0

sampled with probabilities

$S$1

Training images are zero-padded by $S$2 pixels per side; for $S$3, padding is 96 pixels.

The principal comparison is to FastMRI-EDM, a whole-image diffusion model with about 65M parameters, and to PICS-L1, a classical convex reconstruction with wavelet sparsity in BART. PaDIS-MRI is reported to be more computationally expensive despite having fewer parameters: FastMRI-EDM stabilizes at roughly 650 checkpoints in about 2 days, whereas PaDIS-MRI stabilizes at roughly 1451 checkpoints in about 4.5 days, both on a single NVIDIA RTX A6000. Inference time is approximately 9 minutes for PaDIS-MRI and 5 minutes for FastMRI-EDM. The method’s claim is therefore not lower runtime, but greater data efficiency.

5. Quantitative performance, uncertainty, and clinical reader study

At acceleration factor $S$4, averaged over the 82-slice evaluation set, PaDIS-MRI outperforms FastMRI-EDM across the smallest training regimes. At $S$5, PaDIS-MRI attains PSNR 32.97, SSIM 0.847, and NRMSE 0.143, compared with 30.51, 0.817, and 0.185 for FastMRI-EDM, and 26.76, 0.587, and 0.281 for PICS-L1. At $S$6, the values are 35.05, 0.866, and 0.110 for PaDIS-MRI versus 32.62, 0.853, and 0.146 for FastMRI-EDM. From 25 to 500 slices, PaDIS-MRI outperforms FastMRI-EDM on all metrics; at 1000 and 2330 slices, it retains better PSNR and NRMSE, while FastMRI-EDM achieves a slight SSIM advantage (Sanda et al., 25 Sep 2025).

The strongest small-data gain occurs at $S$7, where PaDIS-MRI exceeds FastMRI-EDM by $S$8 dB PSNR, $S$9 SSIM, and $F$0 NRMSE on average paired differences. This is the paper’s central evidence for data efficiency. The same pattern appears in contrast-specific analyses. For T1/FLAIR at $F$1, PaDIS-MRI records 33.46 / 0.840 / 0.138 at $F$2 and 36.45 / 0.865 / 0.096 at $F$3, whereas FastMRI-EDM records 31.82 / 0.803 / 0.162 and 35.43 / 0.869 / 0.108. For T2 at $F$4, the comparison is 32.66 / 0.852 / 0.146 versus 29.67 / 0.826 / 0.200 at $F$5, and 34.62 / 0.872 / 0.113 versus 33.65 / 0.875 / 0.126 at $F$6.

Robustness to severe undersampling is examined by training with $F$7 and evaluating at $F$8. PaDIS-MRI and FastMRI-EDM are similar at $F$9, with PSNR 40.34 and 40.39, but the gap widens as undersampling increases: at $P$0, PaDIS-MRI achieves 35.88 versus 33.87; at $P$1, 34.42 versus 31.61; and at $P$2, 32.82 versus 30.09. The interpretation provided is that patch priors preserve fine anatomy better when k-space information is scarce.

Uncertainty is approximated through reconstruction variability across 10 random undersampling masks at fixed $P$3. Over 17 images, the average pixelwise standard deviation for PaDIS-MRI is consistently lower than for FastMRI-EDM: 0.070 versus 0.075 at $P$4, 0.064 versus 0.078 at $P$5, 0.063 versus 0.072 at $P$6, 0.062 versus 0.069 at $P$7, 0.064 versus 0.068 at $P$8, and 0.062 versus 0.068 at $P$9. In a cross-contrast generalization experiment, models trained only on T2-weighted images and tested on T1 and FLAIR at $\epsilon$0 produce 33.90 / 0.835 / 0.128 for PaDIS-MRI versus 31.36 / 0.784 / 0.171 for FastMRI-EDM at $\epsilon$1, and 35.02 / 0.852 / 0.112 versus 31.69 / 0.780 / 0.166 at $\epsilon$2.

The clinical reader study is a notable component of the evaluation. Three board-certified radiologists reviewed 60 cases, each containing ground truth, PaDIS-MRI reconstruction, FastMRI-EDM reconstruction, and PICS-L1 reconstruction, with randomized and anonymized display order. By image-level majority vote, PaDIS-MRI was preferred in $\epsilon$3 of cases, with 95% CI $\epsilon$4. The preference rate was $\epsilon$5 for the 25-slice models and $\epsilon$6 for the 500-slice models. By contrast, preference rates were $\epsilon$7 for T1/FLAIR and $\epsilon$8 for T2. Radiologists specifically noted diagnostic interchangeability with ground truth, absence of hallucinated or missed structures, and sharpness.

6. Position within diffusion MRI reconstruction and stated limitations

PaDIS-MRI is best understood as an MRI-specific extension of PaDIS rather than a standalone departure from patch-based diffusion inverse solving. The original PaDIS framework proposed learning whole-image priors through position-aware patch diffusion models for inverse problems, emphasizing memory efficiency, data efficiency, and modular insertion into different diffusion inverse solvers. PaDIS-MRI carries that logic into complex-valued, multi-coil accelerated MRI and supplies an explicit clinical comparison against a strong whole-image diffusion baseline (Hu et al., 2024, Sanda et al., 25 Sep 2025).

Within diffusion MRI reconstruction more broadly, a useful comparison is with MotionDPS, which applies the same general posterior-sampling recipe to a richer latent-operator inverse problem. MotionDPS jointly estimates the motion-free 3D image, rigid-body motion parameters, and coil sensitivity maps from motion-corrupted k-space, whereas PaDIS-MRI assumes the MRI forward model is fixed and reconstructs the image alone. This suggests that PaDIS-MRI occupies the data-efficient, image-only branch of diffusion MRI reconstruction, while methods such as MotionDPS extend diffusion posterior inference to joint image, motion, and coil estimation (Ortiz-Gonzalez et al., 21 May 2026).

The limitations stated for PaDIS-MRI are specific and consequential. First, computational cost remains substantial: training is slower and inference longer than FastMRI-EDM. Second, performance gains plateau beyond about 200 slices, which the authors suggest may reflect either an earlier ceiling for patch priors or limited anatomical diversity when larger datasets are formed from adjacent slices of the same volumes. Third, patch factorization plus Monte Carlo offset averaging may not capture global structure as directly as whole-image priors, which is consistent with the slight SSIM edge observed for FastMRI-EDM at larger $\epsilon$9. Fourth, the experiments are confined to FastMRI brain and do not establish generalization to other anatomies, other scanner vendors, different acquisition protocols, or pathology-rich external datasets. Finally, despite the blinded reader study, the evaluation remains retrospective and broader validation would be required for deployment.

A plausible implication is that PaDIS-MRI’s principal significance lies less in claiming universal superiority of patch priors than in showing that local anatomical statistics, when combined with positional encoding and DPS, can yield quantitatively stronger and radiologist-preferred accelerated MRI reconstructions under pronounced data scarcity. In that sense, PaDIS-MRI is a methodologically specific demonstration that, for low-data multi-coil MRI, the choice of prior factorization can be as important as the diffusion sampler itself.