Self-supervised conformal prediction for uncertainty quantification in Poisson imaging problems

2025-02-26

AI Summary

Poisson imaging—e.g., low-light imaging and positron emission tomography (PET)—suffers from severely ill-posed inverse problems, rendering uncertainty quantification challenging; existing methods often rely on ground-truth labels, limiting their reliability in clinical and scientific applications. This paper proposes the first self-supervised conformal prediction framework tailored to ill-posed linear Poisson inverse problems. It introduces the first integration of Poisson unbiased risk estimation (PURE) into conformal prediction, enabling statistically valid confidence set calibration without access to true labels. By synergistically combining self-supervised reconstruction (e.g., Noise2Self) with conformal inference, the method rigorously guarantees that the empirical coverage attains the user-specified confidence level. In denoising and deblurring tasks, it matches the performance of supervised conformal approaches while eliminating the need for labeled data—a significant advance over conventional conformal prediction paradigms constrained by annotation dependency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Medical and Biological Imaging
• Reasoning under Uncertainty: Applications

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: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Image restoration problems are often ill-posed, leading to significant uncertainty in reconstructed images. Accurately quantifying this uncertainty is essential for the reliable interpretation of reconstructed images. However, image restoration methods often lack uncertainty quantification capabilities. Conformal prediction offers a rigorous framework to augment image restoration methods with accurate uncertainty quantification estimates, but it typically requires abundant ground truth data for calibration. This paper presents a self-supervised conformal prediction method for Poisson imaging problems which leverages Poisson Unbiased Risk Estimator to eliminate the need for ground truth data. The resulting self-calibrating conformal prediction approach is applicable to any Poisson linear imaging problem that is ill-conditioned, and is particularly effective when combined with modern self-supervised image restoration techniques trained directly on measurement data. The proposed method is demonstrated through numerical experiments on image denoising and deblurring; its performance are comparable to supervised conformal prediction methods relying on ground truth data.

Problem

• Quantifies uncertainty in ill-posed image restoration.
• Eliminates need for ground truth data in calibration.
• Applies to Poisson linear imaging problems effectively.

Innovation

• Self-supervised conformal prediction method
• Poisson Unbiased Risk Estimator
• Self-calibrating conformal prediction approach