# Functional Neural Networks for Parametric Image Restoration Problems

arXiv: https://arxiv.org/abs/2111.00361 · HTML: https://mlsanity.com/paper/2111.00361/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 71 references that are in the map.
- First posted on arXiv 30 Oct 2021.

## Builds on (most cited first, 30 of 38)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [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)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Recovering Realistic Texture in Image Super-resolution by Deep Spatial Feature Transform](https://mlsanity.com/paper/1804.02815/) (2018)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Toward Convolutional Blind Denoising of Real Photographs](https://mlsanity.com/paper/1807.04686/) (2018)
- [Single Image Super-Resolution via a Holistic Attention Network](https://mlsanity.com/paper/2008.08767/) (2020)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [MemNet: A Persistent Memory Network for Image Restoration](https://mlsanity.com/paper/1708.02209/) (2017)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Real Image Denoising with Feature Attention](https://mlsanity.com/paper/1904.07396/) (2019)
- [Semantic Image Inpainting with Deep Generative Models](https://mlsanity.com/paper/1607.07539/) (2016)
- [Compression Artifacts Reduction by a Deep Convolutional Network](https://mlsanity.com/paper/1504.06993/) (2015)
- [Variable Rate Deep Image Compression With a Conditional Autoencoder](https://mlsanity.com/paper/1909.04802/) (2019)
- [Quantization Guided JPEG Artifact Correction](https://mlsanity.com/paper/2004.09320/) (2020)
- [Deep Network Interpolation for Continuous Imagery Effect Transition](https://mlsanity.com/paper/1811.10515/) (2018)
- [Loss Functions for Neural Networks for Image Processing](https://mlsanity.com/paper/1511.08861/) (2015)
- [Non-Local Color Image Denoising with Convolutional Neural Networks](https://mlsanity.com/paper/1611.06757/) (2016)

## Built on by (most cited first, 9 of 9)

- [Learning Degradation-Independent Representations for Camera ISP Pipelines](https://mlsanity.com/paper/2307.00761/) (2023)
- [Exploring Resolution and Degradation Clues as Self-supervised Signal for Low Quality Object Detection](https://mlsanity.com/paper/2208.03062/) (2022)
- [Learning Task-Oriented Flows to Mutually Guide Feature Alignment in Synthesized and Real Video Denoising](https://mlsanity.com/paper/2208.11803/) (2022)
- [Devil is in the Uniformity: Exploring Diverse Learners within Transformer for Image Restoration](https://mlsanity.com/paper/2503.20174/) (2025)
- [Tunable Convolutions with Parametric Multi-Loss Optimization](https://mlsanity.com/paper/2304.00898/) (2023)
- [Fast Point Cloud Geometry Compression with Context-based Residual Coding and INR-based Refinement](https://mlsanity.com/paper/2408.02966/) (2024)
- [Self-Supervised Face Image Restoration with a One-Shot Reference](https://mlsanity.com/paper/2203.03005/) (2022)
- [Revealing Microscopic Objects in Fluorescence Live Imaging by Video-to-video Translation Based on A Spatial-temporal Generative Adversarial Network](https://mlsanity.com/paper/2502.16342/) (2025)
- [ENAF: A Multi-Exit Network with an Adaptive Patch Fusion for Large Image Super Resolution](https://mlsanity.com/paper/2608.15349/) (2026)

## Abstract (arXiv)

Almost every single image restoration problem has a closely related parameter, such as the scale factor in super-resolution, the noise level in image denoising, and the quality factor in JPEG deblocking. Although recent studies on image restoration problems have achieved great success due to the development of deep neural networks, they handle the parameter involved in an unsophisticated way. Most previous researchers either treat problems with different parameter levels as independent tasks, and train a specific model for each parameter level; or simply ignore the parameter, and train a single model for all parameter levels. The two popular approaches have their own shortcomings. The former is inefficient in computing and the latter is ineffective in performance. In this work, we propose a novel system called functional neural network (FuncNet) to solve a parametric image restoration problem with a single model. Unlike a plain neural network, the smallest conceptual element of our FuncNet is no longer a floating-point variable, but a function of the parameter of the problem. This feature makes it both efficient and effective for a parametric problem. We apply FuncNet to super-resolution, image denoising, and JPEG deblocking. The experimental results show the superiority of our FuncNet on all three parametric image restoration tasks over the state of the arts.