# Training Implicit Networks for Image Deblurring using Jacobian-Free Backpropagation

arXiv: https://arxiv.org/abs/2402.02065 · HTML: https://mlsanity.com/paper/2402.02065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 3 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Monotone operator equilibrium networks](https://mlsanity.com/paper/2006.08591/) (2020)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [On the Theory of Implicit Deep Learning: Global Convergence with Implicit Layers](https://mlsanity.com/paper/2102.07346/) (2021)
- [SHINE: SHaring the INverse Estimate from the forward pass for bi-level optimization and implicit models](https://mlsanity.com/paper/2106.00553/) (2021)
- [Learning the optimal Tikhonov regularizer for inverse problems](https://mlsanity.com/paper/2106.06513/) (2021)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Joint inference and input optimization in equilibrium networks](https://mlsanity.com/paper/2111.13236/) (2021)
- [Explainable AI via Learning to Optimize](https://mlsanity.com/paper/2204.14174/) (2022)
- [Enhanced CNN for image denoising](https://mlsanity.com/paper/1810.11834/) (2018)

## Abstract (arXiv)

Recent efforts in applying implicit networks to solve inverse problems in imaging have achieved competitive or even superior results when compared to feedforward networks. These implicit networks only require constant memory during backpropagation, regardless of the number of layers. However, they are not necessarily easy to train. Gradient calculations are computationally expensive because they require backpropagating through a fixed point. In particular, this process requires solving a large linear system whose size is determined by the number of features in the fixed point iteration. This paper explores a recently proposed method, Jacobian-free Backpropagation (JFB), a backpropagation scheme that circumvents such calculation, in the context of image deblurring problems. Our results show that JFB is comparable against fine-tuned optimization schemes, state-of-the-art (SOTA) feedforward networks, and existing implicit networks at a reduced computational cost.