Training Implicit Networks for Image Deblurring using Jacobian-Free Backpropagation

TL;DR

This work tackles image deblurring with implicit networks, which offer fixed memory but traditionally require costly backprop through a fixed point. By applying Jacobian-Free Backpropagation (JFB), the authors replace the costly Jacobian inverse with an identity, maintaining a descent direction while reducing computational burden. Experiments on a CelebA-derived blurred dataset show competitive PSNR/SSIM with faster gradient steps compared to Jacobian-based training, demonstrating practical efficiency and ease of use. The approach broadens the applicability of implicit networks to real-time or resource-constrained inverse problems and suggests potential extensions to other imaging tasks.

Abstract

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.