# Learning Deep Gradient Descent Optimization for Image Deconvolution

arXiv: https://arxiv.org/abs/1804.03368 · HTML: https://mlsanity.com/paper/1804.03368/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

## Built on by (most cited first, 18 of 18)

- [Deep Image Deblurring: A Survey](https://mlsanity.com/paper/2201.10700/) (2022)
- [DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring](https://mlsanity.com/paper/2103.09962/) (2021)
- [Gaussian Kernel Mixture Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2111.00454/) (2021)
- [Image Deblurring by Exploring In-depth Properties of Transformer](https://mlsanity.com/paper/2303.15198/) (2023)
- [INFWIDE: Image and Feature Space Wiener Deconvolution Network for Non-blind Image Deblurring in Low-Light Conditions](https://mlsanity.com/paper/2207.08201/) (2022)
- [On Adversarial Robustness of Deep Image Deblurring](https://mlsanity.com/paper/2210.02502/) (2022)
- [End-to-end Learning for Joint Depth and Image Reconstruction from Diffracted Rotation](https://mlsanity.com/paper/2204.07076/) (2022)
- [A Design Space Study for LISTA and Beyond](https://mlsanity.com/paper/2104.04110/) (2021)
- [Learning Discriminative Shrinkage Deep Networks for Image Deconvolution](https://mlsanity.com/paper/2111.13876/) (2021)
- [NBD-GAP: Non-Blind Image Deblurring Without Clean Target Images](https://mlsanity.com/paper/2209.09498/) (2022)
- [Leveraging Classic Deconvolution and Feature Extraction in Zero-Shot Image Restoration](https://mlsanity.com/paper/2310.02097/) (2023)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [DeepRLS: A Recurrent Network Architecture with Least Squares Implicit Layers for Non-blind Image Deconvolution](https://mlsanity.com/paper/2112.05505/) (2021)
- [Robust retrieval of material chemical states in X-ray microspectroscopy](https://mlsanity.com/paper/2308.04207/) (2023)
- [Deep Learning and Bayesian inference for Inverse Problems](https://mlsanity.com/paper/2308.15492/) (2023)
- [Deep Learning and Inverse Problems](https://mlsanity.com/paper/2309.00802/) (2023)
- [A Model-Guided Neural Network Method for the Inverse Scattering Problem](https://mlsanity.com/paper/2512.10123/) (2025)
- [Physen-Noise2Noise: Physics-Guided Self-Supervised Defocus Deblurring with Bias Correction under Low-Light Conditions](https://mlsanity.com/paper/2605.24590/) (2026)

## Abstract (arXiv)

As an integral component of blind image deblurring, non-blind deconvolution removes image blur with a given blur kernel, which is essential but difficult due to the ill-posed nature of the inverse problem. The predominant approach is based on optimization subject to regularization functions that are either manually designed, or learned from examples. Existing learning based methods have shown superior restoration quality but are not practical enough due to their restricted and static model design. They solely focus on learning a prior and require to know the noise level for deconvolution. We address the gap between the optimization-based and learning-based approaches by learning a universal gradient descent optimizer. We propose a Recurrent Gradient Descent Network (RGDN) by systematically incorporating deep neural networks into a fully parameterized gradient descent scheme. A hyper-parameter-free update unit shared across steps is used to generate updates from the current estimates, based on a convolutional neural network. By training on diverse examples, the Recurrent Gradient Descent Network learns an implicit image prior and a universal update rule through recursive supervision. The learned optimizer can be repeatedly used to improve the quality of diverse degenerated observations. The proposed method possesses strong interpretability and high generalization. Extensive experiments on synthetic benchmarks and challenging real-world images demonstrate that the proposed deep optimization method is effective and robust to produce favorable results as well as practical for real-world image deblurring applications.