Arbitrary-Scale Anisotropic 3D MRI Super-Resolution with Gaussian Prototypes

Aditya Rastogi; Ramon Leiser; Prateek Singh; Martha Foltyn-Dumitru; Martin Bendszus; Fabian Bamberg; Klaus Maier-Hein; Kai Schlamp

cs.CVOct 17, 2026

Arbitrary-Scale Anisotropic 3D MRI Super-Resolution with Gaussian Prototypes

Authors: Aditya Rastogi, Ramon Leiser, Prateek Singh, Martha Foltyn-Dumitru, Martin Bendszus, Fabian Bamberg, Klaus Maier-Hein, Kai Schlamp,

Abstract

Reducing MRI acquisition time improves patient comfort, reduces motion artefacts, and increases scanner throughput. Clinical protocols often shorten acquisitions by sacrificing spatial resolution, particularly along the slice axis. Super-resolution can recover higher-resolution images, but existing methods are typically specialised to one scale or acquisition geometry, limiting their use across heterogeneous clinical protocols. We present GSMR3D, a continuous volumetric model that reconstructs arbitrary isotropic and anisotropic resolutions with a single checkpoint per MRI contrast. It combines a learned dictionary of anisotropic 3D Gaussian prototypes with scale-conditioned frequency encoding and an exact measurement-consistency projection, keeping reconstructions consistent with the acquired low-resolution data. We train separate models on 3,731 contrast-enhanced T1-weighted and 30,254 T1-weighted brain MRI volumes from clinical and population-based cohorts. We evaluate GSMR3D against geometry-specific specialists for isotropic, in-plane, and through-plane super-resolution using reconstruction quality and downstream tasks: brain tumour segmentation, brain-metastasis detection, and brain parcellation. GSMR3D outperforms specialists at isotropic $2\times$ and achieves better LPIPS, DISTS, and FID across all geometries, although specialists retain higher PSNR in anisotropic settings. It more faithfully preserves glioma segmentations across all geometries, achieves the highest lesion sensitivity on an independent brain-metastasis cohort, and the highest brain-parcellation agreement for isotropic and in-plane reconstruction. Reconstruction takes about 6s per volume, adding little overhead relative to acquisition-time savings. GSMR3D offers a flexible approach to MRI scan-time reduction with one model per contrast across geometries while preserving information relevant to downstream tasks.

Figures & tables

Figure 1: GSMR3D overview. The LR volume ${\bm{X}}$ is encoded into features ${\bm{F}}$ , prototype logits ${\bm{Z}}$ , and coefficient and frequency maps ${\bm{A}}$ and ${\bm{\Omega}}$ respectively. For each HR query ${\bm{x}}$ , features from a fixed $3{\times}3{\times}3$ LR neighbourhood are gathered using anisotropic Gaussians selected from a learned $K{=}512$ prototype dictionary. The gathered features are combined with scale-conditioned Fourier features and decoded into a residual, which is combined with a gated trilinear LR skip and refined. A final training-free projection enforces measurement consistency under the assumed degradation operator, producing the SR reconstruction $\hat{{\bm{Y}}}$ at the desired resolution.

	Isotropic $2\times$			In-plane $2\times$			Through-plane $3\times$			Through-plane $4\times$
Method	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
GSMR3D (ours)	32.50	0.029	5.6	32.69	0.020	3.7	32.95	0.025	7.2	30.86	0.045	10.8
Diffusion + DC	31.84	0.045	6.3	32.89	0.031	4.4	33.14	0.038	10.3	30.69	0.060	12.8
Specialist	32.24	0.043	9.4	33.72	0.027	4.1	34.36	0.036	11.2	31.92	0.059	16.2
Cubic	26.98	0.147	20.8	28.22	0.106	15.2	29.12	0.118	23.3	27.33	0.162	31.4
ResCNN	32.47	0.045	8.2	33.73	0.029	5.3	33.50	0.038	12.7	31.15	0.061	17.0

Table 1: Contrast-enhanced T1 (brain-tumour cohort,

n=100

). Specialists are ArSSR, LTE, and SAINT for isotropic, in-plane, and through-plane SR, respectively. Best in bold; additional results are in Appendix C (Table A4 ).

Table 3

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A1: Detailed GSMR3D architecture. Top: the LR volume is processed by a frozen MAISI stem and a trainable residual adapter, preserving the LR grid while producing the feature volume ${\bm{F}}$ . Separate heads predict prototype logits ${\bm{Z}}$ , gather features ${\bm{F}}_{g}$ , and coefficient and frequency maps ${\bm{A}}$ and ${\bm{\Omega}}$ . Middle: at each LR voxel, the prototype logits select and blend elements of a shared dictionary of $K{=}512$ anisotropic 3D Gaussians in Cholesky space, yielding a local Gaussian with positive-definite covariance. Bottom: for each HR query coordinate ${\bm{x}}$ , features from a fixed $3{\times}3{\times}3$ LR neighbourhood are weighted by the selected Gaussians and gathered into ${\bm{\gamma}}({\bm{x}})$ . The sampled coefficient and frequency maps form scale-conditioned Fourier features, which are fused with ${\bm{\gamma}}({\bm{x}})$ and decoded by an MLP. The resulting residual is combined with a gated trilinear LR skip and passed through a zero-initialised refinement head. The reconstructed queries are assembled on the target grid, and a final a projection enforces measurement consistency under the assumed degradation operator.

		Agreement Dice $\uparrow$			Dice vs. GT $\uparrow$			Vol. err. (%) $\downarrow$
Geometry	Method	CE	NE	WT	CE	NE	WT	CE	WT
Iso $2\times$	GSMR3D (ours)	0.961	0.993	0.994	0.796	0.911	0.927	0.5	0.3
	Diffusion prior + DC	0.946	0.991	0.992	0.791	0.910	0.926	0.9	0.5
	ArSSR (specialist)	0.955	0.990	0.992	0.800	0.911	0.927	0.9	0.4
	TV	0.941	0.987	0.989	0.789	0.909	0.926	1.7	0.8
	Cubic	0.859	0.962	0.968	0.764	0.900	0.920	13.7	2.0

Appendix

Table A7: Full downstream tumour-segmentation results on contrast-enhanced T1-weighted images from the held-out multicentre brain-tumour cohort using HD-GLIO. Agreement is the Dice score between segmentations obtained from the SR and HR volumes. vs. GT is the Dice score against expert annotations. For reference, HD-GLIO applied to the HR images achieves 0.802, 0.911, and 0.927 for CE, NE, and WT, respectively. Vol. err. is the median absolute relative error in tumour volume with respect to the HR-derived segmentation. The best result in each column and geometry is shown in bold.

		Agreement Dice $\uparrow$		Lesion detection (vs. HR)			Vol. err. (%) $\downarrow$
Geometry	Method	CE	FL	Sens. $\uparrow$	Missed $\downarrow$	FP/case $\downarrow$	CE
Iso $2\times$	GSMR3D (ours)	0.939	0.978	0.994	4	0.03	2.2
	Diffusion prior + DC	0.927	0.981	0.982	12	0.02	3.6
	ArSSR (specialist)	0.927	0.966	0.984	11	0.04	2.6
	TV	0.918	0.960	0.976	16	0.03	4.1
	Cubic	0.852	0.911	0.964	24	0.24	14.7

Appendix

Table A9: Downstream brain-metastasis evaluation on the held-out cohort (

n{=}100

, 670 enhancing metastases) using HD-BM. Agreement is measured between SR- and HR-derived segmentations for enhancing metastases (CE) and FLAIR abnormalities (FL). Lesion sensitivity, missed lesions, false positives per case, and enhancing-volume error are evaluated relative to the HR-derived segmentation. Best results for each geometry are shown in bold.

Figure A2: Qualitative CT1 comparison across the four degradation geometries (tumour cohort). Columns show the LR input, cubic interpolation, TV, the geometry-specific specialist (ArSSR, LTE, or SAINT), ResCNN, GSMR3D, and the HR reference. Each reconstruction is accompanied by an enlarged view of the indicated region. Values denote per-case PSNR3D.

Figure A3: Qualitative T1 comparison across the four degradation geometries (Healthy subject). The layout follows Figure A2 .

Figure A4: HD-GLIO tumour segmentation at different geometries . Yellow and red contours indicate whole and contrast-enhancing tumour, respectively. Dice scores for reconstructed images measure agreement with the segmentation obtained from the HR volume, while the HR score measures agreement with the expert annotation.

Figure A5: Brain-metastasis preservation across acquisition geometries. Representative CT1 images from a brain-metastasis case with 70 HR-derived lesions. Red boxes indicate detected reference lesions and blue boxes indicate lesions missed on the displayed slice. For the HR image, Slice and Volume give the number of reference lesions on the displayed slice and in the complete volume. For reconstructed images, these values give the number of detected reference lesions relative to the corresponding HR counts. A lesion missed on the displayed slice may still be detected on a neighbouring slice and therefore counted as detected at the volume level. Volume-level values correspond to the lesion-detection analysis in Table A9 .

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