Physics-Informed Image Restoration via Progressive PDE Integration

TL;DR

The paper tackles motion deblurring by embedding a PDE-based global layer, modeled as advection-diffusion dynamics with a source term, into state-of-the-art restoration networks. A progressive training strategy is introduced to stabilize multi-iteration PDE solvers, enabling effective global feature evolution at the bottleneck while preserving efficiency. Empirical results across GoPro, RealBlur-R, and RealBlur-J show consistent PSNR/SSIM gains (up to ~1 dB PSNR and ~0.007 SSIM) with only about 1% overhead across architectures like FFTformer, NAFNet, Restormer, and Stripformer. This work demonstrates that physics-informed priors can enhance image restoration without substantial computational cost, highlighting a promising direction for integrating PDEs into deep learning for vision tasks.

Abstract

Motion blur, caused by relative movement between camera and scene during exposure, significantly degrades image quality and impairs downstream computer vision tasks such as object detection, tracking, and recognition in dynamic environments. While deep learning-based motion deblurring methods have achieved remarkable progress, existing approaches face fundamental challenges in capturing the long-range spatial dependencies inherent in motion blur patterns. Traditional convolutional methods rely on limited receptive fields and require extremely deep networks to model global spatial relationships. These limitations motivate the need for alternative approaches that incorporate physical priors to guide feature evolution during restoration. In this paper, we propose a progressive training framework that integrates physics-informed PDE dynamics into state-of-the-art restoration architectures. By leveraging advection-diffusion equations to model feature evolution, our approach naturally captures the directional flow characteristics of motion blur while enabling principled global spatial modeling. Our PDE-enhanced deblurring models achieve superior restoration quality with minimal overhead, adding only approximately 1\% to inference GMACs while providing consistent improvements in perceptual quality across multiple state-of-the-art architectures. Comprehensive experiments on standard motion deblurring benchmarks demonstrate that our physics-informed approach improves PSNR and SSIM significantly across four diverse architectures, including FFTformer, NAFNet, Restormer, and Stripformer. These results validate that incorporating mathematical physics principles through PDE-based global layers can enhance deep learning-based image restoration, establishing a promising direction for physics-informed neural network design in computer vision applications.

Figures (2)

• Figure 1: High-level architecture of the image restoration network. The network follows a U-Net style encoder-decoder structure, where the input degraded image y is progressively downsampled through encoder blocks (Encoder Block 1 to N) via max pooling operations. At the bottleneck, global layers process the latent representation at the coarsest scale. The decoder path progressively upsamples the features through decoder blocks (Decoder Block N to 1) using upward convolutions to reconstruct the restored image x*. Skip connections between corresponding encoder and decoder blocks preserve spatial information across scales. The global layers at the bottleneck serve as the primary location for integrating physics-informed processing.
• Figure 2: The Global Layer using PDE models motion blur through learned parameters (u, v), blur kernel f, and diffusion coefficients (Dx, Dy). Progressive increase of iteration steps K during training maintains constant total time T while improving computational efficiency, following the diffusion PDE framework of kag2022.