  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.
