# Enhancing Multi-Scale Implicit Learning in Image Super-Resolution with Integrated Positional Encoding

arXiv: https://arxiv.org/abs/2112.05756 · HTML: https://mlsanity.com/paper/2112.05756/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 10 Dec 2021.

## Builds on (most cited first, 30 of 39)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [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)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [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)
- [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)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [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)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)

## Built on by (most cited first, 13 of 13)

- [Cascaded Local Implicit Transformer for Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2303.16513/) (2023)
- [Local Implicit Normalizing Flow for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2303.05156/) (2023)
- [Continuous Remote Sensing Image Super-Resolution based on Context Interaction in Implicit Function Space](https://mlsanity.com/paper/2302.08046/) (2023)
- [CycleINR: Cycle Implicit Neural Representation for Arbitrary-Scale Volumetric Super-Resolution of Medical Data](https://mlsanity.com/paper/2404.04878/) (2024)
- [BF-STVSR: B-Splines and Fourier-Best Friends for High Fidelity Spatial-Temporal Video Super-Resolution](https://mlsanity.com/paper/2501.11043/) (2025)
- [Local Implicit Wavelet Transformer for Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2411.06442/) (2024)
- [Scale-Invariant Adversarial Attack against Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2503.04385/) (2025)
- [Test-time Cost-and-Quality Controllable Arbitrary-Scale Super-Resolution with Variable Fourier Components](https://mlsanity.com/paper/2412.05517/) (2024)
- [Multi-Scale Implicit Transformer with Re-parameterize for Arbitrary-Scale Super-Resolution](https://mlsanity.com/paper/2403.06536/) (2024)
- [FreqINR: Frequency Consistency for Implicit Neural Representation with Adaptive DCT Frequency Loss](https://mlsanity.com/paper/2408.13716/) (2024)
- [Fidelity- and Perception-Aware Local Implicit Attention for Arbitrary-Scale Image Super-Resolution](https://mlsanity.com/paper/2606.21910/) (2026)
- [Aperture: Merge-Consistent Rotary States for Compressed Tokens](https://mlsanity.com/paper/2609.36781/) (2026)
- [Any-scale Object Detection using Arbitrary-scaled Images](https://mlsanity.com/paper/2610.04346/) (2026)

## Abstract (arXiv)

Is the center position fully capable of representing a pixel? There is nothing wrong to represent pixels with their centers in a discrete image representation, but it makes more sense to consider each pixel as the aggregation of signals from a local area in an image super-resolution (SR) context. Despite the great capability of coordinate-based implicit representation in the field of arbitrary-scale image SR, this area's nature of pixels is not fully considered. To this end, we propose integrated positional encoding (IPE), extending traditional positional encoding by aggregating frequency information over the pixel area. We apply IPE to the state-of-the-art arbitrary-scale image super-resolution method: local implicit image function (LIIF), presenting IPE-LIIF. We show the effectiveness of IPE-LIIF by quantitative and qualitative evaluations, and further demonstrate the generalization ability of IPE to larger image scales and multiple implicit-based methods. Code will be released.