Self-supervised Conformal Prediction for Uncertainty Quantification in Imaging Problems

TL;DR

This paper introduces a self-supervised conformal prediction method using Stein's Unbiased Risk Estimator to quantify uncertainty in image restoration tasks without relying on ground truth data, improving robustness and accuracy.

Contribution

It develops a novel self-supervised conformal prediction framework that bypasses the need for ground truth, enhancing uncertainty quantification in ill-conditioned imaging inverse problems.

Findings

Achieves accurate uncertainty estimates comparable to supervised methods.

Effective in image denoising and deblurring tasks.

Robust to distribution shifts between calibration and deployment.

Abstract

Most image restoration problems are ill-conditioned or ill-posed and hence involve significant uncertainty. Quantifying this uncertainty is crucial for reliably interpreting experimental results, particularly when reconstructed images inform critical decisions and science. However, most existing image restoration methods either fail to quantify uncertainty or provide estimates that are highly inaccurate. Conformal prediction has recently emerged as a flexible framework to equip any estimator with uncertainty quantification capabilities that, by construction, have nearly exact marginal coverage. To achieve this, conformal prediction relies on abundant ground truth data for calibration. However, in image restoration problems, reliable ground truth data is often expensive or not possible to acquire. Also, reliance on ground truth data can introduce large biases in situations of distribution shift between calibration and deployment. This paper seeks to develop a more robust approach to conformal prediction for image restoration problems by proposing a self-supervised conformal prediction method that leverages Stein's Unbiased Risk Estimator (SURE) to self-calibrate itself directly from the observed noisy measurements, bypassing the need for ground truth. The method is suitable for any linear imaging inverse problem that is ill-conditioned, and it is especially powerful when used with modern self-supervised image restoration techniques that can also be trained directly from measurement data. The proposed approach is demonstrated through numerical experiments on image denoising and deblurring, where it delivers results that are remarkably accurate and comparable to those obtained by supervised conformal prediction with ground truth data.