# Dual-Prior Guided Null-Space Learning with Mixture-of-Splines for Arbitrary Medical Slice Super-Resolution

arXiv: https://arxiv.org/abs/2606.26716 · HTML: https://mlsanity.com/paper/2606.26716/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [CiaoSR: Continuous Implicit Attention-in-Attention Network for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2212.04362/) (2022)
- [Super-Resolution Neural Operator](https://mlsanity.com/paper/2303.02584/) (2023)
- [An Arbitrary Scale Super-Resolution Approach for 3D MR Images via Implicit Neural Representation](https://mlsanity.com/paper/2110.14476/) (2021)
- [SAINT: Spatially Aware Interpolation NeTwork for Medical Slice Synthesis](https://mlsanity.com/paper/2001.00704/) (2020)
- [Spline Positional Encoding for Learning 3D Implicit Signed Distance Fields](https://mlsanity.com/paper/2106.01553/) (2021)
- [Latent Modulated Function for Computational Optimal Continuous Image Representation](https://mlsanity.com/paper/2404.16451/) (2024)
- [HIIF: Hierarchical Encoding based Implicit Image Function for Continuous Super-resolution](https://mlsanity.com/paper/2412.03748/) (2024)
- [RPLHR-CT Dataset and Transformer Baseline for Volumetric Super-Resolution from CT Scans](https://mlsanity.com/paper/2206.06253/) (2022)
- [CycleINR: Cycle Implicit Neural Representation for Arbitrary-Scale Volumetric Super-Resolution of Medical Data](https://mlsanity.com/paper/2404.04878/) (2024)
- [DiffFNO: Diffusion Fourier Neural Operator](https://mlsanity.com/paper/2411.09911/) (2024)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)
- [BF-STVSR: B-Splines and Fourier-Best Friends for High Fidelity Spatial-Temporal Video Super-Resolution](https://mlsanity.com/paper/2501.11043/) (2025)
- [Spatial Attention-based Implicit Neural Representation for Arbitrary Reduction of MRI Slice Spacing](https://mlsanity.com/paper/2205.11346/) (2022)
- [I3Net: Inter-Intra-slice Interpolation Network for Medical Slice Synthesis](https://mlsanity.com/paper/2405.02857/) (2024)
- [NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems](https://mlsanity.com/paper/2510.01608/) (2025)
- [An Anisotropic Cross-View Texture Transfer with Multi-Reference Non-Local Attention for CT Slice Interpolation](https://mlsanity.com/paper/2509.20242/) (2025)

## Abstract (arXiv)

Arbitrary slice super-resolution reconstructs isotropic volumes from anisotropic clinical acquisitions by synthesizing intermediate slices at arbitrary scales. However, treating this ill-posed inverse problem as unconstrained residual-based regression risks hallucinating anatomically implausible structures or altering the originally observed data. To address both concerns, this paper presents the Dual-Prior Null-space Learning (DP-NSL) framework, which reformulates the task as a constrained recovery process guided by two complementary priors. A Measurement-Consistent Projection (MCP) enforces a Deterministic Observation Prior: the reconstruction undergoes an exact orthogonal projection that reproduces every acquired slice with zero error, confining all learned details to the unobservable null space. Within this null space, a Mixture-of-Splines (MoS) module imposes a Geometric Continuity Prior by dynamically mixing B-spline experts of different analytic orders, allowing each anatomical region to be modeled with a content-aware level of continuity. To promote spatial coherence, a Local Spatial Consistency Decoder (LSCD) further injects local inductive bias. Experiments on three CT and one MRI benchmark show that DP-NSL outperforms existing approaches while strictly preserving measurement consistency. Code is available at https://github.com/DeepMed-Lab-ECNU/Medical-Image-Reconstruction.