# OPE-SR: Orthogonal Position Encoding for Designing a Parameter-free Upsampling Module in Arbitrary-scale Image Super-Resolution

arXiv: https://arxiv.org/abs/2303.01091 · HTML: https://mlsanity.com/paper/2303.01091/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 85 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [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)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [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)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [FDA: Fourier Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2004.05498/) (2020)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)

## Built on by (most cited first, 17 of 17)

- [Latent Modulated Function for Computational Optimal Continuous Image Representation](https://mlsanity.com/paper/2404.16451/) (2024)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)
- [Arbitrary-Scale Video Super-Resolution with Structural and Textural Priors](https://mlsanity.com/paper/2407.09919/) (2024)
- [Exploring the Low-Pass Filtering Behavior in Image Super-Resolution](https://mlsanity.com/paper/2405.07919/) (2024)
- [Training-Free Model Ensemble for Single-Image Super-Resolution via Strong-Branch Compensation](https://mlsanity.com/paper/2604.11564/) (2026)
- [Rotation Equivariant Arbitrary-scale Image Super-Resolution](https://mlsanity.com/paper/2508.05160/) (2025)
- [Implicit Neural Feature Fusion Function for Multispectral and Hyperspectral Image Fusion](https://mlsanity.com/paper/2307.07288/) (2023)
- [Learning Dual-Level Deformable Implicit Representation for Real-World Scale Arbitrary Super-Resolution](https://mlsanity.com/paper/2403.10925/) (2024)
- [AnySR: Realizing Image Super-Resolution as Any-Scale, Any-Resource](https://mlsanity.com/paper/2407.04241/) (2024)
- [Test-time Cost-and-Quality Controllable Arbitrary-Scale Super-Resolution with Variable Fourier Components](https://mlsanity.com/paper/2412.05517/) (2024)
- [Q2A: Querying Implicit Fully Continuous Feature Pyramid to Align Features for Medical Image Segmentation](https://mlsanity.com/paper/2404.09472/) (2024)
- [LeRF: Learning Resampling Function for Adaptive and Efficient Image Interpolation](https://mlsanity.com/paper/2407.09935/) (2024)
- [Your Super Resolution Model is not Enough for Tackling Real-World Scenarios](https://mlsanity.com/paper/2509.06387/) (2025)
- [OmniScaleSR: Unleashing Scale-Controlled Diffusion Prior for Faithful and Realistic Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2512.04699/) (2025)
- [Continuous Filtered Backprojection by Learnable Interpolation Network](https://mlsanity.com/paper/2505.01768/) (2025)
- [BasicAVSR: Arbitrary-Scale Video Super-Resolution via Image Priors and Enhanced Motion Compensation](https://mlsanity.com/paper/2510.26149/) (2025)
- [GB-LSR: Local Spectral Decoding with a Learned Global Bandwidth for Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2606.19617/) (2026)

## Abstract (arXiv)

Implicit neural representation (INR) is a popular approach for arbitrary-scale image super-resolution (SR), as a key component of INR, position encoding improves its representation ability. Motivated by position encoding, we propose orthogonal position encoding (OPE) - an extension of position encoding - and an OPE-Upscale module to replace the INR-based upsampling module for arbitrary-scale image super-resolution. Same as INR, our OPE-Upscale Module takes 2D coordinates and latent code as inputs; however it does not require training parameters. This parameter-free feature allows the OPE-Upscale Module to directly perform linear combination operations to reconstruct an image in a continuous manner, achieving an arbitrary-scale image reconstruction. As a concise SR framework, our method has high computing efficiency and consumes less memory comparing to the state-of-the-art (SOTA), which has been confirmed by extensive experiments and evaluations. In addition, our method has comparable results with SOTA in arbitrary scale image super-resolution. Last but not the least, we show that OPE corresponds to a set of orthogonal basis, justifying our design principle.