Self-supervised Conformal Prediction for Uncertainty Quantification in Imaging Problems

TL;DR

The paper tackles uncertainty quantification in ill-posed image restoration by marrying conformal prediction with self-supervised calibration. It introduces a SURE-based calibration scheme that replaces ground-truth calibration, enabling reliable prediction sets for $C(Y)$ defined via $s(x,y) = \frac{1}{m}\|A x - A \hat{x}(y)\|^2$ and $C(y) = \{ x: s(x,y) \le q_\alpha \}$. The method pools multiple exchangeable imaging problems and uses Hutchinson's trace estimator to compute the required divergence for SURE, enabling scalable, parallelizable UQ for both model-based and data-driven restorers. Experiments on image denoising and non-blind deblurring show that SURE-based conformal prediction achieves empirical coverage comparable to supervised conformal prediction, demonstrating robustness to distribution shifts and practical applicability when ground-truth data are unavailable. This approach expands reliable uncertainty quantification in imaging where ground-truth labels are scarce or shifting, with potential extensions to other noise models and non-full-rank forwards.

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.

Figures (4)

• Figure 1: Image reconstruction results for various imaging problems. Top: Gaussian noise on DIV2K. Bottom: Noisy Gaussian blur on DIV2K
• Figure 2: Image denoising experiment: desired confidence level vs empirical coverage. Both supervised and the proposed self-supervised conformal prediction methods deliver prediction sets with near perfect coverage.
• Figure 3: Image deblurring experiment: desired confidence level vs empirical coverage. Both supervised and the proposed self-supervised conformal prediction methods deliver prediction sets with near perfect coverage.
• Figure 4: Calibration histograms (empirical distribution of the non-similarity function $s(x,y)$) for the supervised case (MSE) and the self-supervised case based on a SURE estimate of the MSE, for the denoising and deblurring experiments.