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

TL;DR

The paper introduces a conformal-prediction framework to bound the full-reference image-quality $z_0=m(\widehat{x}_0,x_0)$ of a recovered image in imaging inverse problems without access to the ground-truth $x_0$. By leveraging approximate posterior sampling, it constructs adaptive bounds (quantile and learned via quantile regression) that calibrate on a separate dataset to guarantee $\Pr\{ Z_0 \in {\mathcal C}_{\widehat{\lambda}}(\widehat{Z}_0) \} \ge 1-\alpha$, with $\widehat{Z}_0=f(u_0)$ encoding test measurements and reconstruction. The authors demonstrate the approach on image denoising (FFHQ) and accelerated MRI (fastMRI knee), showing that adaptive bounds closely track the true FRIQ while maintaining the coverage guarantee, and enabling multi-round measurement strategies to improve throughput. This provides rigorous uncertainty quantification for perceptual image-quality metrics like PSNR, SSIM, LPIPS, and DISTS, with potential to enhance safety-critical imaging decisions.

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.

Figures (23)

• Figure 1: Overview of method: Given a recovery $\widehat{x}_0$ of true image $x_0$, approximate posterior samples $\{ \widetilde{x}_0^{{(j)}} \}_{j=1}^{c}$, and a calibration set $d_{\mathsf{cal}}$, we construct a prediction interval $\mathcal{C}_{\widehat{\lambda}(d_{\mathsf{cal}})}(\widehat{z}_0 )$ that is guaranteed to contain the unknown true FRIQ $z_0=m(\widehat{x}_0,x_0)$ with probability at least $1-\alpha$.
• Figure 2: Scatter plots show the non-adaptive (purple) and quantile (green) bounds $\beta(\widehat{z}_k, \widehat{\lambda}(d_{\mathsf{cal}}[t]))$ versus the true FRIQ $z_k$ over FFHQ test samples $k$. The black line shows where $\beta=z$, and a fraction $\alpha=0.05$ of samples are on the side of the line that violates the bound. The quantile bound tracks the true $z_k$ much better than the non-adaptive bound. The red and blue stars correspond to the images in the red and blue boxes: the red recovery represents better FRIQs and blue represents worse.
• Figure 3: Examples from the FFHQ denoising experiment. Top row: true image and low-LPIPS recovery. Bottom row: true image and high-LPIPS recovery. True LPIPS reported in blue and quantile upper-bound in red. (Recall that LPIPS assigns lower values to better recoveries.)
• Figure 4: Mean conformal bound versus number of posterior samples $c$ for FFHQ denoising.
• Figure 5: Mean absolute difference between the bound and true FRIQ versus number of posterior samples $c$ for FFHQ denoising.