Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction

TL;DR

This paper introduces a task-driven conformal prediction framework for uncertainty quantification in inverse imaging problems, especially in MRI, providing guaranteed interval estimates for downstream task outputs.

Contribution

It develops a novel conformal prediction method tailored for inverse problems, incorporating task-specific uncertainty quantification and adaptive measurement collection.

Findings

Constructs guaranteed prediction intervals for task outputs in inverse problems.

Provides locally adaptive intervals for posterior-sampling-based image recovery.

Demonstrates effectiveness on accelerated MRI with adaptive measurement stopping.

Abstract

In imaging inverse problems, one seeks to recover an image from missing/corrupted measurements. Because such problems are ill-posed, there is great motivation to quantify the uncertainty induced by the measurement-and-recovery process. Motivated by applications where the recovered image is used for a downstream task, such as soft-output classification, we propose a task-centered approach to uncertainty quantification. In particular, we use conformal prediction to construct an interval that is guaranteed to contain the task output from the true image up to a user-specified probability, and we use the width of that interval to quantify the uncertainty contributed by measurement-and-recovery. For posterior-sampling-based image recovery, we construct locally adaptive prediction intervals. Furthermore, we propose to collect measurements over multiple rounds, stopping as soon as the task uncertainty falls below an acceptable level. We demonstrate our methodology on accelerated magnetic resonance imaging (MRI): https://github.com/jwen307/TaskUQ.