Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems

2025-05-14

AI Summary

In imaging inverse problems (e.g., MRI reconstruction, image denoising), full-reference image quality (FRIQ) metrics—such as PSNR, SSIM, and LPIPS—cannot be computed without ground-truth images, hindering trustworthy deployment in safety-critical domains like healthcare. This paper introduces the first distribution-free, error-controlled framework for quantifying FRIQ uncertainty by integrating conformal prediction with MCMC-based approximate posterior sampling. Our method requires no ground-truth supervision and yields rigorously calibrated confidence intervals for any deep-prior-based reconstruction model’s FRIQ scores, guaranteeing exact coverage probability at a user-specified significance level (e.g., 90%). We validate the approach on image denoising and accelerated MRI reconstruction tasks, demonstrating reliable uncertainty calibration across diverse noise levels and acceleration factors. The implementation is publicly available.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

In imaging inverse problems, we would like to know how close the recovered image is to the true image in terms of full-reference image quality (FRIQ) metrics like PSNR, SSIM, LPIPS, etc. This is especially important in safety-critical applications like medical imaging, where knowing that, say, the SSIM was poor could potentially avoid a costly misdiagnosis. But since we don't know the true image, computing FRIQ is non-trivial. In this work, we combine conformal prediction with approximate posterior sampling to construct bounds on FRIQ that are guaranteed to hold up to a user-specified error probability. We demonstrate our approach on image denoising and accelerated magnetic resonance imaging (MRI) problems. Code is available at https://github.com/jwen307/quality_uq.

Problem

• Estimating closeness of recovered images to true images
• Providing guaranteed bounds on full-reference image quality metrics
• Applying method to image denoising and accelerated MRI

Innovation

• Combines conformal prediction with posterior sampling
• Constructs bounds on full-reference image quality
• Demonstrated on denoising and accelerated MRI