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

TL;DR

This paper introduces a self-supervised conformal prediction method for Poisson imaging that provides reliable uncertainty quantification without requiring ground truth data, applicable to ill-conditioned image restoration tasks.

Contribution

It develops a novel self-supervised conformal prediction framework using Poisson Unbiased Risk Estimator, enabling uncertainty quantification without ground truth in Poisson imaging.

Findings

Performance comparable to supervised methods

Effective in denoising and deblurring tasks

Applicable to ill-conditioned problems

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.