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

TL;DR

This work tackles uncertainty quantification in Poisson imaging inverse problems by extending conformal prediction to Poisson noise without requiring ground-truth calibration. It introduces a self-supervised framework that uses the Poisson Unbiased Risk Estimator (PURE) with a split-conformal non-conformity $s(x,y)=\frac{1}{m}\|A x - A x\_hat(y)\|^2$ and a calibration scheme based on PURE-based quantiles; the method leverages measurement-driven self-supervised restorers trained directly on data. The approach is validated on Poisson image denoising and non-blind deblurring with DIV2K data, achieving prediction-set coverage close to nominal levels and competitive performance relative to fully supervised conformal prediction. By removing the ground-truth calibration bottleneck and leveraging measurement-based training, the method provides robust uncertainty quantification suitable for scientific imaging and decision-support tasks.

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.

Figures (4)

• Figure 1: PURE-based conformal prediction
• Figure 2: Image reconstruction results for image denoising (top) and non-blind image deblurring (bottom), by using a self-supervised neural-network estimator $\hat{x}(y)$ and images from DIV2K.
• Figure 3: Poisson image denoising experiment: desired confidence level vs empirical coverage; the proposed self-supervised conformal prediction methods deliver prediction sets with near perfect coverage.
• Figure 4: Poisson image deblurring experiment: desired confidence level vs empirical coverage; the proposed self-supervised conformal prediction methods deliver prediction sets with near perfect coverage.