PhyMRI-SR: Toward Physics-Aware MRI Image Super-Resolution

Lihua Wei; Huatong Gao; Jia Gong; Zhiyu Tan; Hao Li; Jun Liu; Zhihua Ren

Source-linked AI summary

PhyMRI-SR: Toward Physics-Aware MRI Image Super-Resolution

Lihua Wei, Huatong Gao, Jia Gong, Zhiyu Tan, Hao Li, Jun Liu, Zhihua Ren

arXiv:2607.06238v1Jul 7, 2026cs.CV

TL;DR

MRI super-resolution often assumes a fixed low-resolution input despite acquisition-dependent resolution–SNR trade-offs. PhyMRI-SR formulates reconstruction as physics-aware, resolution-agnostic 2D Gaussian Splatting and achieves state-of-the-art performance across dynamic-resolution datasets and benchmarks.

Problem
MRI super-resolution must account for acquisition-dependent resolution–SNR trade-offs rather than treating every scan as a fixed-resolution input.
Method
PhyMRI-SR uses resolution-agnostic 2D Gaussian Splatting with anatomical and imaging-system priors, physics-constrained tissue modeling, and simulated-to-real meta-learning.
Results
The method consistently outperforms baselines across dynamic-resolution datasets, static-resolution benchmarks, and real multi-resolution data on quantitative and qualitative evaluations.
Takeaways & Limitations
The experiments support selecting an intermediate optimal resolution rather than assuming the highest achievable input resolution is best for MRI super-resolution.

Abstract

from arXiv · show

Magnetic resonance imaging (MRI) super-resolution is vital for improving diagnostic accessibility, yet most methods treat it as a deterministic mapping from a fixed low-resolution input to a high-resolution target. This overlooks a key property of MRI acquisition physics: spatial resolution and signal-to-noise ratio (SNR) are inherently coupled, making any given low-resolution scan merely one of many possible realizations under varying acquisition trade-offs. We rethink MRI super-resolution as a physics-aware reconstruction problem, in which the goal is to identify the optimal resolution-SNR configuration and then super-resolve it to obtain high-quality MRI results. A key implication of this formulation is that MRI resolution becomes dynamic rather than fixed. To handle such resolution-heterogeneous inputs, we adapt 2D Gaussian Splatting (2D GS) to MRI by formulating reconstruction as a coordinate-based, resolution-agnostic rendering problem. To further enhance fidelity, we introduce three innovations: (1) a prior-aware Gaussian representation that combines an Anatomical Structure Prior for tissue-specific kernel initialization with an Imaging System Prior that captures hardware characteristics via a covariance dictionary; (2) a physics-constrained signal modeling scheme that predicts intrinsic tissue parameters (proton density rho and effective relaxation rate R2) and synthesizes intensities through governing physical equations, ensuring biophysically plausible contrast; and (3) a meta-learning framework that alleviates paired-data scarcity by pretraining on simulated data and adapting to real-world conditions. Extensive experiments on dynamic-resolution datasets and standard benchmarks demonstrate that our method achieves state-of-the-art performance, highlighting its strong potential for clinical deployment.

I. INTRODUCTION … B. Continuous Super-Resolution

The paper reframes MRI super-resolution as physics-aware reconstruction that accounts for the coupled resolution–SNR acquisition trade-off, rather than deterministic upscaling from fixed-resolution inputs. It adapts 2D Gaussian Splatting to provide continuous, resolution-agnostic reconstruction for heterogeneous MRI inputs.

I. INTRODUCTION: The proposed framework formulates MRI super-resolution as physics-aware reconstruction that explicitly models resolution, SNR, and sampling-efficiency trade-offs during acquisition.This reframing treats the input scan as one realization among many possible acquisition configurations rather than as an optimal static starting point.
I. INTRODUCTION: The method adapts 2D Gaussian Splatting by representing MRI as a continuous signal and rendering arbitrary-dimensional low-resolution inputs into a unified continuous Gaussian field.Coordinate-based rendering replaces operation on a fixed-size pixel grid, supporting dynamic input resolution.
I. INTRODUCTION: Prior-aware Gaussian representation combines anatomical and imaging-system priors to allocate tissue-specific kernels and capture hardware-dependent global patterns.The Anatomical Structure Prior concentrates capacity in complex regions such as cortical folds, while the Imaging System Prior represents characteristics including point spread functions through system-specific structure.
I. INTRODUCTION: Physics-constrained signal modeling predicts proton density ρ and effective relaxation rate R2, then synthesizes intensities through governing physical equations.This avoids direct pixel-intensity regression and enforces biophysically plausible contrast relationships.
A. MRI Super Resolution: MRI acquisition trades spatial resolution against SNR and scan time, making high-resolution imaging costly while low-resolution scans may lack diagnostic detail.High-resolution imaging typically requires longer scans to maintain SNR, whereas low-resolution imaging is faster and may improve SNR but loses detail.
I. INTRODUCTION: Existing MRI super-resolution methods predominantly map a specific low-resolution input to a fixed high-resolution target without modeling the acquisition system or resolution–SNR trade-off.The paper identifies this deterministic, fixed-scale formulation as a central limitation of prior work.
B. Continuous Super-Resolution: Traditional super-resolution methods target discrete integer scales such as ×2, ×4, or ×8, requiring separate models for different factors and limiting continuous-resolution flexibility.These design choices increase computational cost and are poorly suited to continuous resolutions in real-world scenarios.
B. Continuous Super-Resolution: 2D Gaussian Splatting has emerged as an alternative for continuous super-resolution, and the paper adapts it to MRI with a prior-aware Gaussian representation.The paper contrasts this approach with implicit methods that struggle to capture continuous signal structures and require time-consuming upsampling and decoding.

III. PRELIMINARY · A. Resolution-SNR Trade-off in MRI · B. 2D Gaussian Splatting for Super-Resolution

MRI resolution and SNR are intrinsically coupled because smaller voxels reduce signal while acquisition noise remains approximately voxel-size independent, motivating dynamic-resolution super-resolution. 2D Gaussian Splatting provides a continuous, resolution-agnostic representation for arbitrary-scale reconstruction, but MRI applications require domain-specific priors, biophysical constraints, and strategies for scarce paired data.

A. Resolution-SNR Trade-off in MRI: Smaller voxels increase spatial resolution but reduce MRI signal amplitude approximately in proportion to voxel volume.Voxel signal aggregates proton contributions, with S_voxel scaling approximately linearly with V_voxel for small voxel dimensions.
A. Resolution-SNR Trade-off in MRI: The resulting resolution–SNR relationship directly affects MRI image quality and motivates searching for an optimal-resolution image before super-resolution.The formulation is derived from MRI signal and noise equations, using Spin Echo as a clinical example and incorporating proton density and relaxation parameters.
A. Resolution-SNR Trade-off in MRI: Acquisition noise remains approximately independent of voxel size and decreases mainly through signal averaging and longer acquisition time.The relevant acquisition factors are the number of repetitions, N_ex, and acquisition time, T_acq.
B. 2D Gaussian Splatting for Super-Resolution: 2D Gaussian Splatting represents images with continuous geometric primitives, enabling arbitrary-scale super-resolution without retraining.Its resolution-agnostic representation avoids restricting reconstruction to a fixed discrete pixel grid.
B. 2D Gaussian Splatting for Super-Resolution: The 2D GS pipeline encodes low-resolution inputs, predicts Gaussian properties from continuous features, and renders the high-resolution output.The features capture local texture and global structure, while rendering can produce images on target coordinate grids at arbitrary scales.
B. 2D Gaussian Splatting for Super-Resolution: Gaussian color parameters model intensity, whereas covariance matrices control each primitive’s spatial extent and orientation for anisotropic local-structure modeling.The covariance matrices are defined in R^2×2, and the differentiable renderer supports end-to-end optimization with paired LR–HR data.
B. 2D Gaussian Splatting for Super-Resolution: Directly applying 2D GS to MRI is challenged by missing anatomical and imaging-system priors, which can yield geometrically unreliable primitives and weak structural coherence.The limitation concerns position and covariance estimation without domain-specific guidance.
B. 2D Gaussian Splatting for Super-Resolution: MRI applications also face biophysical implausibility from unconstrained intensity prediction and scarcity of paired low- and high-resolution images.These issues can compromise downstream analysis and make effective model optimization difficult.

IV. METHOD · A. Prior-Aware Gaussian Representation · 1) Anatomical structure guided initialization and refinement:

The method reframes MRI super-resolution as continuous-scale, physics-aware Gaussian splatting for inputs spanning the resolution-SNR spectrum. Its prior-aware representation uses anatomical guidance to allocate and refine Gaussian primitives while preserving structural fidelity.

IV. METHOD: The framework targets dynamic adjustment across the resolution-SNR spectrum, where continuous-resolution 2D Gaussian Splatting supports MRI super-resolution.Vanilla 2D GS is unsuitable without additional domain-specific guidance.
A. Prior-Aware Gaussian Representation: The prior-aware Gaussian representation introduces domain-specific priors to improve anatomical structural fidelity and clarity.It is one of three targeted innovations in the physics-aware Gaussian splatting framework.
A. Prior-Aware Gaussian Representation: The method addresses Gaussian initialization and covariance parameterization using anatomical structure and imaging system fingerprint priors.These priors replace unguided spatial positioning and natural-image covariance assumptions with MRI-specific guidance.
1) Anatomical structure guided initialization and refinement:: Gaussian primitives are allocated using density weights that jointly reflect each tissue region’s spatial extent and structural complexity.The predefined complexity ordering is wGM > wWM > wCSF.
1) Anatomical structure guided initialization and refinement:: A tissue segmentation mask partitions the image into K regions, such as cerebrospinal fluid, gray matter, white matter, and background.The segmentator provides the anatomical regions used for initialization.
1) Anatomical structure guided initialization and refinement:: The anatomy-guided allocation concentrates sampling density in larger, structurally complex tissues, producing a more faithful and efficient brain representation.The design gives tissues such as gray matter more representational capacity than simpler regions such as CSF.
1) Anatomical structure guided initialization and refinement:: A position refinement module predicts per-primitive offsets from extracted features, adapting anatomically initialized locations to patient-specific image content.The tanh function constrains normalized offsets to [−1, 1], while δ limits displacement to [−δ, δ].

2) Image system-prior based Covariance optimization: · B. Physics-Constrained Signal Modeling · 1) Signal Formation Model:

The method optimizes MRI-realistic Gaussian covariance geometry using an imaging-system prior, then predicts intensities from tissue properties and acquisition physics. Its signal model uses proton density and effective relaxation to represent T2-weighted contrast.

2) Image system-prior based Covariance optimization:: Gaussian covariance geometry reflects both anatomical structure and MRI acquisition characteristics, motivating an MRI-specific covariance dictionary.The dictionary captures hardware-specific patterns such as acquisition artifacts and point spread functions.
2) Image system-prior based Covariance optimization:: The covariance dictionary is built from fitted high-resolution brain MRI primitives and empirical covariance distributions distinct from natural images.It contains M representative covariance matrices sampled from those distributions.
2) Image system-prior based Covariance optimization:: During super-resolution, the covariance module predicts combination weights over dictionary elements instead of directly predicting covariance entries.This constrains covariance estimates to MRI-realistic configurations while preserving flexibility for diverse anatomical structures.
B. Physics-Constrained Signal Modeling: Physics-constrained signal modeling predicts intensities from tissue relaxation properties and local proton density rather than treating intensity as arbitrary.The approach is motivated by Bloch-equation-governed MRI formation and seeks to preserve expected tissue contrast relationships.
1) Signal Formation Model:: MRI signal intensity depends on tissue-specific relaxation properties and acquisition parameters, with T2-weighted formation expressed through proton density, T1, T2, TR, and TE.The signal formation model is introduced as the physical basis for the method’s intensity prediction.
1) Signal Formation Model:: For typical T2-weighted acquisitions, sufficiently long TR makes the T1-dependent term approach unity, simplifying the signal model.This condition isolates the dominant contrast behavior used for T2-weighted intensity prediction.
1) Signal Formation Model:: The simplified model uses R2 = TE/T2 as an effective relaxation term and captures the dominant contrast mechanism in T2-weighted images.This equation provides the physical basis for predicting reconstructed intensities.

2) Tissue Parameter Prediction: … B. Experimental Setup

PhyMRI-SR predicts intrinsic tissue parameters and derives intensities through a physics-constrained signal model, while meta-learning adapts representations across simulated and real low-field conditions. Experiments evaluate dynamic- and static-resolution reconstruction using simulated and real MRI datasets with established comparison methods.

2) Tissue Parameter Prediction:: The method decomposes intensity prediction into proton density ρ and effective relaxation R2 for each Gaussian primitive instead of directly regressing pixel intensities.Each primitive is interpreted as a localized proton spin ensemble.
2) Tissue Parameter Prediction:: A physics-constrained intensity layer synthesizes each primitive’s intensity from its predicted tissue parameters, with a learnable residual accommodating modeling and acquisition imperfections.The residual captures effects omitted by the idealized signal equation.
2) Tissue Parameter Prediction:: Because ρ and R2 are resolution-independent tissue properties, the decomposition promotes biophysically plausible contrast and resolution-invariant representations across super-resolution scales.This formulation is intended to improve generalization across different scales.
C. Model Training and Meta-Learning for Domain Adaptation: The training pipeline combines a large simulated low-field dataset with limited paired real low-field data, using segmentation masks as anatomical priors during synthetic pretraining.The simulated data include multiple resolution-SNR configurations of 64mT images.
C. Model Training and Meta-Learning for Domain Adaptation: Episodic meta-training learns a shared initialization that rapidly adapts to unseen low-field conditions with only a few gradient steps, jointly leveraging simulated and real data.This replaces a fixed low-to-high-field mapping with rapid adaptation to novel degradation conditions.
A. Implementation Details: Experiments use T2-weighted 3T IXI scans as ground truth and simulate 64mT low-resolution inputs at scales 1.0, 0.9, 0.7, 0.5, and 0.25.The simulated scales represent varying spatial resolutions for 64mT field MRI.
A. Implementation Details: Implementation uses SwinIR as encoder, 2D U-Net as segmentator, Adam optimization, combined L1, gradient, and frequency losses, batch size 4, and 1,000 epochs.The initial learning rate is 1×10^-4 and decays by 0.5 every 100 epochs on one NVIDIA RTX 4090 GPU.

C. Evaluation results … D. Ablation Study

The evaluation uses complementary fidelity, structural, perceptual, and high-frequency metrics, showing that optimal input resolution is dynamic and that the method outperforms baselines on simulated and real MRI data. Ablations further support the contributions of initialization, physics-constrained modeling, and meta-learning.

1) Evaluation metrics.:: The evaluation combines PSNR, SSIM, DISTS, and HFEN to measure pixel fidelity, structural consistency, perceptual quality, and fine structural recovery.HFEN uses a Laplacian of Gaussian filter.
2) Results on dynamic resolution:: At ×0.7 on simulated IXI, the method achieves 28.10 dB PSNR, 0.9234 SSIM, 0.3051 HFEN, and 0.1148 DISTS, best across scales.It outperforms three baselines across all resolution scales and metrics.
2) Results on dynamic resolution:: The method exhibits non-monotonic resolution–performance behavior, with ×0.76 achieving the lowest real-data HFEN of 0.4570 and competitive other metrics.This supports that the highest input resolution is not always optimal for super-resolution.
2) Results on dynamic resolution:: At ×0.7, reconstructions show the sharpest edges and richest structural details, whereas ×1.0 amplifies noise and ×0.25 loses unrecoverable structure.Both simulated and real multi-resolution experiments support a dynamic optimal resolution.
3) Results on static resolution:: At 4× on static benchmarks, the method reaches 34.26 dB PSNR and 0.962 SSIM, surpassing MS-PRDDiff by 1.45 dB and 0.020.Across 4×, 5×, and 6.4× scales, it achieves the best performance across all reported metrics.
3) Results on static resolution:: Qualitatively, the method recovers fine anatomical details and preserves cortical folding, white-gray matter boundaries, and ventricular structures consistent with 3T references.Baselines produce over-smoothed or hallucinated structures on real data.
D. Ablation Study: Meta-learning raises PSNR from 19.7 to 25.4 and SSIM from 0.82 to 0.85 versus w/o Meta, while physics removal lowers SSIM from 0.85 to 0.55.Naive initialization raises PSNR from 18.2 to 19.1 but lowers SSIM from 0.71 to 0.68; supplementary results further validate the components.

VI. CONCLUSION · S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI

The paper concludes that MRI super-resolution should identify an appropriate resolution-SNR configuration rather than assume the highest resolution is optimal. Its theoretical background explains this trade-off through Fourier-encoded acquisition, voxel-volume-dependent signal, noise scaling, and acquisition-time costs.

VI. CONCLUSION: The proposed physics-informed 2D Gaussian Splatting framework confirms that the optimal MRI super-resolution input is not necessarily the highest-resolution acquisition.The conclusion reframes low-resolution inputs as potentially suboptimal because MRI image quality varies in both SNR and resolution.
S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI: MRI measures Fourier-encoded signals from a continuous spin distribution, modulated by tissue contrast, coil sensitivity, acquisition trajectory, and noise.The received signal depends on proton density, coil sensitivity, sequence-dependent contrast weighting, k-space trajectory, and acquisition noise.
S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI: Finite k-space coverage reconstructs local PSF-weighted averages rather than ideal point samples, with voxel signal scaling linearly with voxel volume in homogeneous tissue.The voxel model combines PSF averaging with image-domain noise; under locally homogeneous tissue and fixed protocol, signal is proportional to voxel volume.
S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI: With fixed tissue contrast, receiver bandwidth, and averaging, SNR is directly linked to spatial resolution through voxel volume and acquisition noise.Thermal receiver noise is modeled as zero-mean complex Gaussian noise; bandwidth increases noise variance, while Nex averages reduce variance.
S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI: Improving resolution requires extending sampled k-space, reducing voxel dimensions and consequently lowering SNR.Nominal resolution is determined by maximum sampled spatial frequency, so increasing kx,max, ky,max, and kz,max reduces spatial resolutions and voxel volume.
S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI: Doubling isotropic resolution reduces voxel-wise SNR by 8, while restoring the original SNR through averaging requires 64 times more averages.In-plane-only 2D enhancement has milder scaling than isotropic 3D enhancement but still incurs substantial SNR loss.
S1. THEORETICAL BACKGROUND: RESOLUTION-SNR TRADE-OFF IN MRI: Higher-resolution acquisition also increases scan time, creating a fundamental trade-off among spatial resolution, SNR, and acquisition time.This trade-off motivates selecting a resolution that balances anatomical detail and noise robustness instead of pursuing the highest nominal spatial resolution.

S2. DATASET DETAILS

The section details all datasets used in the work, together with their preprocessing pipelines and data splits.

The section covers all datasets used in the work.
It describes the preprocessing pipelines applied to the datasets.
It reports the data splits used for the datasets.

A. IXI-based Simulated Dynamic-Resolution Dataset · 1) Degradation Model for Low-Field MRI Simulation: · B. Real Paired Dataset (64mT–3T)

The study constructs an IXI-based simulated dynamic-resolution dataset from preprocessed 3T MRI and models low-field degradation through resolution loss, noise, and intensity inhomogeneity. Real-world adaptation is evaluated on paired 64mT–3T scans from 11 healthy subjects with subject-level training, validation, and testing splits.

A. IXI-based Simulated Dynamic-Resolution Dataset: T2-weighted 3T IXI MRI scans serve as high-resolution ground truth after standardized preprocessing.The pipeline includes skull stripping, N4 bias-field correction, intensity normalization, and spatial resampling.
A. IXI-based Simulated Dynamic-Resolution Dataset: 1,750 training slices are obtained by uniformly sampling 10 central axial slices per volume after excluding the top and bottom 20%.Corresponding low-resolution images are generated with the low-field degradation model.
1) Degradation Model for Low-Field MRI Simulation:: The low-field simulation combines resolution degradation, additive noise corruption, multiplicative intensity inhomogeneity, brain masking, and intensity clipping.The degradation model uses HR images, resolution degradation D(·), noise n, bias field B, mask M, and clipping C(·).
1) Degradation Model for Low-Field MRI Simulation:: Gaussian PSF blurring models spatial resolution loss, with kernel standard deviation σ controlling degradation severity.The blur parameter σ varies across task-dependent settings for dynamic-resolution simulation and meta-learning.
1) Degradation Model for Low-Field MRI Simulation:: MRI noise is modeled with a Rician distribution using real and imaginary noise components.This explicitly represents the magnitude-image noise process used in the simulated low-field data.
1) Degradation Model for Low-Field MRI Simulation:: The simulated bias field uses Gaussian smoothing, with default strength β = 0.35 and spatial smoothness σb = 25.The blur parameter σ and noise level α remain task-dependent variables.
B. Real Paired Dataset (64mT–3T): The real paired dataset contains 64mT and 3T brain MRI scans from 11 healthy subjects for domain-adaptation validation.It is publicly available and was released by Leiden University Medical Center.
B. Real Paired Dataset (64mT–3T): After matching IXI preprocessing and central-slice sampling, the real data split into 180 training, 60 validation, and 60 testing paired slices.The split uses 6, 2, and 3 subjects, respectively.

C. Real Dynamic-Resolution Dataset (3T–5T) … 2) Task Formulation:

The paper combines real 3T–5T acquisitions, supplementary unpaired 5T data, MRI-specific priors, tissue segmentation, and meta-learning to address dynamic-resolution super-resolution under scarce paired data. Its adaptation tasks span simulated and real degradation domains, with subject-disjoint support and query sets for generalization.

C. Real Dynamic-Resolution Dataset (3T–5T): Paired T2-weighted FSE data were acquired from 10 healthy subjects on 3T and 5T United Imaging scanners.The 5T protocol used TR = 4500 ms, TE = 108 ms, flip angle = 110◦, 5 mm slices, and a 576 × 501 matrix; the 3T protocol used TR = 4545 ms, TE = 120 ms, and flip angle = 145◦.
S3. ADDITIONAL IMPLEMENTATION DETAILS: The acquisition-parameter tables specify 3T scan configurations across different resolution scales, with FOV and matrix-size conventions defined separately.FOV is reported as readout × phase-encoding, while matrix size is reported as Nx × Ny.
D. Supplementary Unpaired 5T Data: Because paired dynamic-resolution acquisition is costly, 18 additional subjects provided unpaired 5T scans used as high-resolution references for synthesizing pseudo-paired 3T images at multiple scales.The synthesis uses the degradation model described in Section S2.11.
A. MRI-Specific Covariance Dictionary Statistics: From 4,241 5T MRI slices, the method fits 2D Gaussian primitives and derives covariance statistics distinct from natural-image distributions.The reported parameter ranges are [0, 2.39], [−0.18, 1.12], and [0, 2.05]; sampling 10 values per parameter yields 1,000 combinations, and adding the zero kernel produces 1,001 kernels.
B. Segmentation Mask Generation: SynthSeg generates contrast-agnostic whole-brain masks for high-resolution MRI, which are consolidated into three primary tissue classes.SynthSeg partitions the brain into 60 anatomical regions and resamples volumetric data to 1×1×1 mm3.
B. Segmentation Mask Generation: A dedicated 2D U-Net predicts three-tissue masks for low-resolution slices from paired high-resolution masks and spatially aligned low-resolution inputs.This enables integration of low-resolution segmentation into the 2D super-resolution framework.
C. Additional details of Domain Adaptation via Meta-Learning: Meta-learning transfers knowledge from simulated degradation domains to real paired 64mT–3T data, enabling adaptation when paired training data is scarce.The framework learns a rapidly adaptable initialization, uses limited real paired data during meta-training, and models variability through episodic tasks.

3) Episodic Meta-Optimization:

The method uses first-order MAML to learn an initialization that adapts rapidly across MRI reconstruction tasks. Episodic training combines diverse simulated degradations with at least one real task per episode, using subject-disjoint support and query slices to anchor adaptation to realistic imaging conditions.

3) Episodic Meta-Optimization:: First-order MAML learns an initialization θ that can rapidly adapt to new reconstruction tasks with few gradient steps.The approximation avoids differentiating through the inner-loop update for computational efficiency.
3) Episodic Meta-Optimization:: Each episode samples a task batch containing at least one real task alongside simulated degradations.This maintains exposure to realistic imaging characteristics while exploiting diverse synthetic degradation patterns.
3) Episodic Meta-Optimization:: For every task, one inner-loop gradient update uses a support set of 2 slices from one subject, followed by query evaluation on 2 slices from a different subject.The support and query sets therefore separate adaptation from evaluation across subjects.
3) Episodic Meta-Optimization:: The outer loop aggregates task-query gradients to update θ, while real-task inclusion anchors optimization to the target distribution and limits drift toward synthetic artifacts.The dual-domain strategy is intended to address real-world MRI data scarcity and promote generalizable super-resolution priors.

S4. ADDITIONAL EXPERIMENT RESULTS … S6. BIOGRAPHY SECTION

Additional experiments show that the method recovers anatomical detail across fastMRI degradation scales and that initialization plus physics modeling improves sharpness, grayscale fidelity, and structural agreement with ground truth. The study also documents ethics procedures and provides author biographies spanning MRI, medical imaging, and broader AI research.

A. More FastMRI Benchmark Results: Across ×4, ×5, and ×6.4 fastMRI degradations, the method recovers fine structures, including the inter-hemispheric fissure missed by PRDDIFF and Pixel-to-Gaussian.Pixel-to-Gaussian produces over-smoothed outputs, whereas PRDDIFF retains residual noise and weaker anatomical fidelity and structural consistency.
B. More Ablation Study Results: The ablation compares LR input, configurations without or with initialization, initialization plus physics, and ground truth.These comparisons isolate the contributions of initialization and the physics module.
B. More Ablation Study Results: Without physics modeling, outputs retain the LR intensity distribution and deviate from ground truth in overall grayscale fidelity.Removing initialization also causes visibly blurred reconstructions with substantially smoothed fine structures.
B. More Ablation Study Results: Initialization partially sharpens internal structures, but the physics module restores the grayscale distribution and improves finer anatomical details consistent with ground truth.The figure likewise reports significantly improved grayscale fidelity and finer structural recovery after adding physics modeling.
S5. ETHICS STATEMENT: The dynamic-resolution 3T-5T paired data were collected under ShanghaiTech University Ethics Committee oversight under Application No. Q2026-015, with written informed consent.The data were anonymized before analysis and used only for research purposes.
S5. ETHICS STATEMENT: The supplementary material includes the original ethics approval document for the study.This document is provided on the following page.
S6. BIOGRAPHY SECTION: Lihua Wei and Huatong Gao are ShanghaiTech biomedical engineering students whose interests include MRI super-resolution, reconstruction, enhancement, synthesis, and medical-imaging AI.Wei is pursuing an M.E. after a 2025 B.E.; Gao is pursuing an M.Eng. after a 2025 B.Eng.
S6. BIOGRAPHY SECTION: The biographies also cover researchers and professors working across computer vision, multimodal AI, video generation, AI for Science, digital health, and MRI physics and instrumentation.They include Jia Gong, Zhiyu Tan, Hao Li, Jun Liu, and Zhihua Ren, with affiliations spanning Shanghai Academy of Artificial Intelligence for Science, Fudan University, Lancaster University, and ShanghaiTech University.