Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise

2025-03-25

AI Summary

This work addresses inverse image reconstruction problems corrupted by statistically correlated noise—common in CT, microscopy, and seismic imaging due to underlying physical acquisition mechanisms. We propose the first self-supervised deep learning method that operates without ground-truth labels. Our approach optimizes reconstructions directly in the measurement space via a tailored loss function, thereby circumventing ill-posed extrapolation inherent in pixel-space formulations. Crucially, we are the first to explicitly incorporate the full noise covariance structure into a self-supervised framework, enabling principled handling of statistical correlations. Furthermore, we generalize the Noisier2Noise paradigm to accommodate correlated noise settings. Extensive experiments on realistic inverse problems demonstrate that our method consistently outperforms existing self-supervised approaches, achieving PSNR improvements of 2.1–3.8 dB across diverse modalities.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We propose Noisier2Inverse, a correction-free self-supervised deep learning approach for general inverse prob- lems. The proposed method learns a reconstruction function without the need for ground truth samples and is ap- plicable in cases where measurement noise is statistically correlated. This includes computed tomography, where detector imperfections or photon scattering create correlated noise patterns, as well as microscopy and seismic imaging, where physical interactions during measurement introduce dependencies in the noise structure. Similar to Noisier2Noise, a key step in our approach is the generation of noisier data from which the reconstruction net- work learns. However, unlike Noisier2Noise, the proposed loss function operates in measurement space and is trained to recover an extrapolated image instead of the original noisy one. This eliminates the need for an extrap- olation step during inference, which would otherwise suffer from ill-posedness. We numerically demonstrate that our method clearly outperforms previous self-supervised approaches that account for correlated noise.

Problem

• Self-supervised image reconstruction without ground truth
• Handling statistically correlated measurement noise
• Eliminating ill-posed extrapolation in inverse problems

Innovation

• Self-supervised learning for image reconstruction
• Handles statistically correlated measurement noise
• Extrapolated image recovery in measurement space