Self-supervised Conformal Prediction for Uncertainty Quantification in Imaging Problems

This paper presents a self-supervised conformal prediction method for uncertainty quantification in imaging problems without ground truth available. 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. However, to achieve this, conformal prediction relies on abundant ground truth data for calibration. In image reconstruction 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. Our proposed method leverages Stein’s Unbiased Risk Estimator to self-calibrate directly from the observed noisy measurements, bypassing the need for ground truth. The method is suitable for any linear inverse problem that is ill-conditioned, and it is especially powerful when used with modern self-supervised imaging techniques that can also be trained directly from measurement data. The proposed approach is demonstrated through image denoising and deblurring experiments, where it delivers results that are remarkably accurate and comparable to those obtained by supervised conformal prediction with ground truth data.