# Self-Organized Operational Neural Networks for Severe Image Restoration Problems

arXiv: https://arxiv.org/abs/2008.12894 · HTML: https://mlsanity.com/paper/2008.12894/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2020.

## Built on by (most cited first, 28 of 28)

- [OSegNet: Operational Segmentation Network for COVID-19 Detection using Chest X-ray Images](https://mlsanity.com/paper/2202.10185/) (2022)
- [COVID-19 Infection Localization and Severity Grading from Chest X-ray Images](https://mlsanity.com/paper/2103.07985/) (2021)
- [Real-Time Patient-Specific ECG Classification by 1D Self-Operational Neural Networks](https://mlsanity.com/paper/2110.02215/) (2021)
- [Real-Time Glaucoma Detection from Digital Fundus Images using Self-ONNs](https://mlsanity.com/paper/2109.13604/) (2021)
- [Robust Peak Detection for Holter ECGs by Self-Organized Operational Neural Networks](https://mlsanity.com/paper/2110.02381/) (2021)
- [Blind ECG Restoration by Operational Cycle-GANs](https://mlsanity.com/paper/2202.00589/) (2022)
- [Global ECG Classification by Self-Operational Neural Networks with Feature Injection](https://mlsanity.com/paper/2204.03768/) (2022)
- [Self-Organized Variational Autoencoders (Self-VAE) for Learned Image Compression](https://mlsanity.com/paper/2105.12107/) (2021)
- [BM3D vs 2-Layer ONN](https://mlsanity.com/paper/2103.03060/) (2021)
- [Super Neurons](https://mlsanity.com/paper/2109.01594/) (2021)
- [NORPPA: NOvel Ringed seal re-identification by Pelage Pattern Aggregation](https://mlsanity.com/paper/2206.02498/) (2022)
- [SRL-SOA: Self-Representation Learning with Sparse 1D-Operational Autoencoder for Hyperspectral Image Band Selection](https://mlsanity.com/paper/2202.09918/) (2022)
- [Zero-Shot Motor Health Monitoring by Blind Domain Transition](https://mlsanity.com/paper/2212.06154/) (2022)
- [DroneNet: Crowd Density Estimation using Self-ONNs for Drones](https://mlsanity.com/paper/2211.07137/) (2022)
- [Blind Restoration of Real-World Audio by 1D Operational GANs](https://mlsanity.com/paper/2212.14618/) (2022)
- [Convolutional versus Self-Organized Operational Neural Networks for Real-World Blind Image Denoising](https://mlsanity.com/paper/2103.03070/) (2021)
- [2D Self-Organized ONN Model For Handwritten Text Recognition](https://mlsanity.com/paper/2207.08139/) (2022)
- [R2C-GAN: Restore-to-Classify Generative Adversarial Networks for Blind X-Ray Restoration and COVID-19 Classification](https://mlsanity.com/paper/2209.14770/) (2022)
- [Operational Support Estimator Networks](https://mlsanity.com/paper/2307.06065/) (2023)
- [Joint End-to-End Image Compression and Denoising: Leveraging Contrastive Learning and Multi-Scale Self-ONNs](https://mlsanity.com/paper/2402.05582/) (2024)
- [Self-DenseMobileNet: A Robust Framework for Lung Nodule Classification using Self-ONN and Stacking-based Meta-Classifier](https://mlsanity.com/paper/2410.12584/) (2024)
- [Thermal Image-based Fault Diagnosis in Induction Machines via Self-Organized Operational Neural Networks](https://mlsanity.com/paper/2412.05901/) (2024)
- [Expert Operational GANS: Towards Real-Color Underwater Image Restoration](https://mlsanity.com/paper/2507.11562/) (2025)
- [CASR-Net: An Image Processing-focused Deep Learning-based Coronary Artery Segmentation and Refinement Network for X-ray Coronary Angiogram](https://mlsanity.com/paper/2510.27315/) (2025)
- [Image denoising by Super Neurons: Why go deep?](https://mlsanity.com/paper/2111.14948/) (2021)
- [Exploring Sound vs Vibration for Robust Fault Detection on Rotating Machinery](https://mlsanity.com/paper/2312.10742/) (2023)
- [High-Quality and Full Bandwidth Seismic Signal Synthesis using Operational GANs](https://mlsanity.com/paper/2407.11040/) (2024)
- [Multi-Pass, Multi-View Blended Learning for High-Fidelity Volumetric CT Synthesis from Chest X-Rays](https://mlsanity.com/paper/2609.09920/) (2026)

## Abstract (arXiv)

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and has outperformed the traditional non-local class of methods. However, the top-performing networks are generally composed of many convolutional layers and hundreds of neurons, with trainable parameters in excess of several millions. We claim that this is due to the inherent linear nature of convolution-based transformation, which is inadequate for handling severe restoration problems. Recently, a non-linear generalization of CNNs, called the operational neural networks (ONN), has been shown to outperform CNN on AWGN denoising. However, its formulation is burdened by a fixed collection of well-known nonlinear operators and an exhaustive search to find the best possible configuration for a given architecture, whose efficacy is further limited by a fixed output layer operator assignment. In this study, we leverage the Taylor series-based function approximation to propose a self-organizing variant of ONNs, Self-ONNs, for image restoration, which synthesizes novel nodal transformations onthe-fly as part of the learning process, thus eliminating the need for redundant training runs for operator search. In addition, it enables a finer level of operator heterogeneity by diversifying individual connections of the receptive fields and weights. We perform a series of extensive ablation experiments across three severe image restoration tasks. Even when a strict equivalence of learnable parameters is imposed, Self-ONNs surpass CNNs by a considerable margin across all problems, improving the generalization performance by up to 3 dB in terms of PSNR.