Image Restoration Learning via Noisy Supervision in the Fourier Domain

2025-05-31

AI Summary

Existing noise-supervised image restoration methods struggle to model spatially correlated noise (e.g., in low-light or remote sensing images) and are limited by the information capacity of pixel-wise losses. This paper proposes a novel Fourier-domain noise supervision paradigm: we first theoretically prove that the Fourier coefficients of various practical noise types asymptotically follow a Gaussian distribution; leveraging this property, we establish frequency-domain equivalence between noisy and clean images, enabling a unified, clean-label-free restoration framework. By incorporating statistical modeling in the Fourier domain and designing differentiable frequency-domain losses, our approach is compatible with diverse deep network architectures. Experiments demonstrate substantial improvements in PSNR and SSIM across multiple image restoration tasks, along with enhanced texture fidelity and perceptual quality. Moreover, our method exhibits superior generalization compared to state-of-the-art noise-supervised approaches.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Unsupervised & Self-Supervised Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Noisy supervision refers to supervising image restoration learning with noisy targets. It can alleviate the data collection burden and enhance the practical applicability of deep learning techniques. However, existing methods suffer from two key drawbacks. Firstly, they are ineffective in handling spatially correlated noise commonly observed in practical applications such as low-light imaging and remote sensing. Secondly, they rely on pixel-wise loss functions that only provide limited supervision information. This work addresses these challenges by leveraging the Fourier domain. We highlight that the Fourier coefficients of spatially correlated noise exhibit sparsity and independence, making them easier to handle. Additionally, Fourier coefficients contain global information, enabling more significant supervision. Motivated by these insights, we propose to establish noisy supervision in the Fourier domain. We first prove that Fourier coefficients of a wide range of noise converge in distribution to the Gaussian distribution. Exploiting this statistical property, we establish the equivalence between using noisy targets and clean targets in the Fourier domain. This leads to a unified learning framework applicable to various image restoration tasks, diverse network architectures, and different noise models. Extensive experiments validate the outstanding performance of this framework in terms of both quantitative indices and perceptual quality.

Problem

• Handling spatially correlated noise in image restoration
• Overcoming limitations of pixel-wise loss functions
• Establishing noisy supervision in Fourier domain

Innovation

• Leveraging Fourier domain for noise handling
• Using Fourier coefficients for global supervision
• Unified learning framework for diverse tasks