# An Arbitrary Scale Super-Resolution Approach for 3D MR Images via Implicit Neural Representation

arXiv: https://arxiv.org/abs/2110.14476 · HTML: https://mlsanity.com/paper/2110.14476/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 27 Oct 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- [Structure-Preserving Super Resolution with Gradient Guidance](https://mlsanity.com/paper/2003.13081/) (2020)
- [Efficient and Accurate MRI Super-Resolution using a Generative Adversarial Network and 3D Multi-Level Densely Connected Network](https://mlsanity.com/paper/1803.01417/) (2018)
- [InfinityGAN: Towards Infinite-Pixel Image Synthesis](https://mlsanity.com/paper/2104.03963/) (2021)
- [Brain MRI Super Resolution Using 3D Deep Densely Connected Neural Networks](https://mlsanity.com/paper/1801.02728/) (2018)
- [Multi-Contrast Super-Resolution MRI Through a Progressive Network](https://mlsanity.com/paper/1908.01612/) (2019)
- [IREM: High-Resolution Magnetic Resonance (MR) Image Reconstruction via Implicit Neural Representation](https://mlsanity.com/paper/2106.15097/) (2021)
- [Joint Implicit Image Function for Guided Depth Super-Resolution](https://mlsanity.com/paper/2107.08717/) (2021)
- [Enhanced generative adversarial network for 3D brain MRI super-resolution](https://mlsanity.com/paper/1907.04835/) (2019)
- [MRI Super-Resolution with GAN and 3D Multi-Level DenseNet: Smaller, Faster, and Better](https://mlsanity.com/paper/2003.01217/) (2020)

## Built on by (most cited first, 30 of 48)

- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [A survey of synthetic data augmentation methods in computer vision](https://mlsanity.com/paper/2403.10075/) (2024)
- [Single-subject Multi-contrast MRI Super-resolution via Implicit Neural Representations](https://mlsanity.com/paper/2303.15065/) (2023)
- [CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution](https://mlsanity.com/paper/2303.16242/) (2023)
- [CycleINR: Cycle Implicit Neural Representation for Arbitrary-Scale Volumetric Super-Resolution of Medical Data](https://mlsanity.com/paper/2404.04878/) (2024)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Uni-COAL: A Unified Framework for Cross-Modality Synthesis and Super-Resolution of MR Images](https://mlsanity.com/paper/2311.08225/) (2023)
- [MicroDiffusion: Implicit Representation-Guided Diffusion for 3D Reconstruction from Limited 2D Microscopy Projections](https://mlsanity.com/paper/2403.10815/) (2024)
- [DISGAN: Wavelet-informed Discriminator Guides GAN to MRI Super-resolution with Noise Cleaning](https://mlsanity.com/paper/2308.12084/) (2023)
- [Continuous 3D Myocardial Motion Tracking via Echocardiography](https://mlsanity.com/paper/2310.02792/) (2023)
- [I3Net: Inter-Intra-slice Interpolation Network for Medical Slice Synthesis](https://mlsanity.com/paper/2405.02857/) (2024)
- [Towards General Text-guided Image Synthesis for Customized Multimodal Brain MRI Generation](https://mlsanity.com/paper/2409.16818/) (2024)
- [ECLARE: Efficient cross-planar learning for anisotropic resolution enhancement](https://mlsanity.com/paper/2503.11787/) (2025)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Super-resolution of biomedical volumes with 2D supervision](https://mlsanity.com/paper/2404.09425/) (2024)
- [UlRe-NeRF: 3D Ultrasound Imaging through Neural Rendering with Ultrasound Reflection Direction Parameterization](https://mlsanity.com/paper/2408.00860/) (2024)
- [Estimating Neural Orientation Distribution Fields on High Resolution Diffusion MRI Scans](https://mlsanity.com/paper/2409.09387/) (2024)
- [Inter-slice Super-resolution of Magnetic Resonance Images by Pre-training and Self-supervised Fine-tuning](https://mlsanity.com/paper/2406.05974/) (2024)
- [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024)
- [Implicit Neural Representations of Intramyocardial Motion and Strain](https://mlsanity.com/paper/2509.09004/) (2025)
- [An Anisotropic Cross-View Texture Transfer with Multi-Reference Non-Local Attention for CT Slice Interpolation](https://mlsanity.com/paper/2509.20242/) (2025)
- [A Three-Player GAN for Super-Resolution in Magnetic Resonance Imaging](https://mlsanity.com/paper/2303.13900/) (2023)
- [Enhance the Image: Super Resolution using Artificial Intelligence in MRI](https://mlsanity.com/paper/2406.13625/) (2024)
- [SeCo-INR: Semantically Conditioned Implicit Neural Representations for Improved Medical Image Super-Resolution](https://mlsanity.com/paper/2409.01013/) (2024)
- [Learning Two-factor Representation for Magnetic Resonance Image Super-resolution](https://mlsanity.com/paper/2409.09731/) (2024)
- [Continuous K-space Recovery Network with Image Guidance for Fast MRI Reconstruction](https://mlsanity.com/paper/2411.11282/) (2024)
- [QFGN: A Quantum Approach to High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2504.19053/) (2025)
- [Zero-shot CT Super-Resolution using Diffusion-based 2D Projection Priors and Signed 3D Gaussians](https://mlsanity.com/paper/2508.15151/) (2025)
- [Physics-Driven 3D Gaussian Rendering for Zero-Shot MRI Super-Resolution](https://mlsanity.com/paper/2603.09621/) (2026)
- [CLADE: Cycle Loss Augmented Degradation Enhancement for Unpaired Super-Resolution of Anisotropic Medical Images](https://mlsanity.com/paper/2303.11831/) (2023)

## Abstract (arXiv)

High Resolution (HR) medical images provide rich anatomical structure details to facilitate early and accurate diagnosis. In MRI, restricted by hardware capacity, scan time, and patient cooperation ability, isotropic 3D HR image acquisition typically requests long scan time and, results in small spatial coverage and low SNR. Recent studies showed that, with deep convolutional neural networks, isotropic HR MR images could be recovered from low-resolution (LR) input via single image super-resolution (SISR) algorithms. However, most existing SISR methods tend to approach a scale-specific projection between LR and HR images, thus these methods can only deal with a fixed up-sampling rate. For achieving different up-sampling rates, multiple SR networks have to be built up respectively, which is very time-consuming and resource-intensive. In this paper, we propose ArSSR, an Arbitrary Scale Super-Resolution approach for recovering 3D HR MR images. In the ArSSR model, the reconstruction of HR images with different up-scaling rates is defined as learning a continuous implicit voxel function from the observed LR images. Then the SR task is converted to represent the implicit voxel function via deep neural networks from a set of paired HR-LR training examples. The ArSSR model consists of an encoder network and a decoder network. Specifically, the convolutional encoder network is to extract feature maps from the LR input images and the fully-connected decoder network is to approximate the implicit voxel function. Due to the continuity of the learned function, a single ArSSR model can achieve arbitrary up-sampling rate reconstruction of HR images from any input LR image after training. Experimental results on three datasets show that the ArSSR model can achieve state-of-the-art SR performance for 3D HR MR image reconstruction while using a single trained model to achieve arbitrary up-sampling scales.