# DeepRLS: A Recurrent Network Architecture with Least Squares Implicit Layers for Non-blind Image Deconvolution

arXiv: https://arxiv.org/abs/2112.05505 · HTML: https://mlsanity.com/paper/2112.05505/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 10 Dec 2021.

## Builds on (most cited first, 12 of 12)

- [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)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Neural Blind Deconvolution Using Deep Priors](https://mlsanity.com/paper/1908.02197/) (2019)
- [Deep linear neural networks with arbitrary loss: All local minima are global](https://mlsanity.com/paper/1712.01473/) (2017)
- [Explore Image Deblurring via Blur Kernel Space](https://mlsanity.com/paper/2104.00317/) (2021)
- [DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring](https://mlsanity.com/paper/2103.09962/) (2021)
- [Iterative Joint Image Demosaicking and Denoising using a Residual Denoising Network](https://mlsanity.com/paper/1807.06403/) (2018)
- [Learning Deep Gradient Descent Optimization for Image Deconvolution](https://mlsanity.com/paper/1804.03368/) (2018)

## Abstract (arXiv)

In this work, we study the problem of non-blind image deconvolution and propose a novel recurrent network architecture that leads to very competitive restoration results of high image quality. Motivated by the computational efficiency and robustness of existing large scale linear solvers, we manage to express the solution to this problem as the solution of a series of adaptive non-negative least-squares problems. This gives rise to our proposed Recurrent Least Squares Deconvolution Network (RLSDN) architecture, which consists of an implicit layer that imposes a linear constraint between its input and output. By design, our network manages to serve two important purposes simultaneously. The first is that it implicitly models an effective image prior that can adequately characterize the set of natural images, while the second is that it recovers the corresponding maximum a posteriori (MAP) estimate. Experiments on publicly available datasets, comparing recent state-of-the-art methods, show that our proposed RLSDN approach achieves the best reported performance both for grayscale and color images for all tested scenarios. Furthermore, we introduce a novel training strategy that can be adopted by any network architecture that involves the solution of linear systems as part of its pipeline. Our strategy eliminates completely the need to unroll the iterations required by the linear solver and, thus, it reduces significantly the memory footprint during training. Consequently, this enables the training of deeper network architectures which can further improve the reconstruction results.