# Learning Two-factor Representation for Magnetic Resonance Image Super-resolution

arXiv: https://arxiv.org/abs/2409.09731 · HTML: https://mlsanity.com/paper/2409.09731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 15 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [An Arbitrary Scale Super-Resolution Approach for 3D MR Images via Implicit Neural Representation](https://mlsanity.com/paper/2110.14476/) (2021)
- [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)
- [Single-subject Multi-contrast MRI Super-resolution via Implicit Neural Representations](https://mlsanity.com/paper/2303.15065/) (2023)
- [Neural Fourier Filter Bank](https://mlsanity.com/paper/2212.01735/) (2022)
- [CuNeRF: Cube-Based Neural Radiance Field for Zero-Shot Medical Image Arbitrary-Scale Super Resolution](https://mlsanity.com/paper/2303.16242/) (2023)
- [MRI Super-Resolution with Ensemble Learning and Complementary Priors](https://mlsanity.com/paper/1907.03063/) (2019)
- [MRI Super-Resolution with GAN and 3D Multi-Level DenseNet: Smaller, Faster, and Better](https://mlsanity.com/paper/2003.01217/) (2020)
- [Deep MR Brain Image Super-Resolution Using Spatio-Structural Priors](https://mlsanity.com/paper/1909.04572/) (2019)
- [SCARF: Scalable Continual Learning Framework for Memory-efficient Multiple Neural Radiance Fields](https://mlsanity.com/paper/2409.04482/) (2024)

## Built on by (most cited first, 1 of 1)

- [SSCM: A Spatial-Semantic Consistent Model for Multi-Contrast MRI Super-Resolution](https://mlsanity.com/paper/2509.18593/) (2025)

## Abstract (arXiv)

Magnetic Resonance Imaging (MRI) requires a trade-off between resolution, signal-to-noise ratio, and scan time, making high-resolution (HR) acquisition challenging. Therefore, super-resolution for MR image is a feasible solution. However, most existing methods face challenges in accurately learning a continuous volumetric representation from low-resolution image or require HR image for supervision. To solve these challenges, we propose a novel method for MR image super-resolution based on two-factor representation. Specifically, we factorize intensity signals into a linear combination of learnable basis and coefficient factors, enabling efficient continuous volumetric representation from low-resolution MR image. Besides, we introduce a coordinate-based encoding to capture structural relationships between sparse voxels, facilitating smooth completion in unobserved regions. Experiments on BraTS 2019 and MSSEG 2016 datasets demonstrate that our method achieves state-of-the-art performance, providing superior visual fidelity and robustness, particularly in large up-sampling scale MR image super-resolution.