Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Prediction.

Area of Science:

• Medical Imaging
• Computational Imaging
• Uncertainty Quantification

Background:

• Image reconstruction from incomplete or corrupted measurements is an ill-posed problem.
• Quantifying uncertainty in the recovered image is crucial for downstream applications like classification.
• Existing methods often lack task-specific uncertainty quantification.

Purpose of the Study:

• To develop a task-centered uncertainty quantification method for image reconstruction.
• To guarantee the accuracy of task outputs derived from reconstructed images.
• To adaptively acquire measurements based on task uncertainty levels.

Main Methods:

• Utilized conformal prediction to construct prediction intervals for task outputs.
• Quantified measurement-and-recovery uncertainty using the width of these intervals.
• Developed locally adaptive prediction intervals for posterior-sampling-based reconstruction.
• Implemented a multi-round measurement acquisition strategy to minimize uncertainty.

Main Results:

• Demonstrated the ability to guarantee task output containment within user-specified probabilities.
• Showcased uncertainty quantification tailored to specific downstream tasks.
• Validated the adaptive measurement strategy on accelerated magnetic resonance imaging (MRI).

Conclusions:

• The proposed task-centered approach effectively quantifies uncertainty in image reconstruction.
• Conformal prediction provides rigorous uncertainty guarantees for downstream tasks.
• Adaptive data acquisition based on task uncertainty can optimize imaging protocols.