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).

在成像逆问题中，通过缺失或损坏的测量数据来恢复图像是一个不适定问题，因此我们提出了一种以任务为中心的方法来量化测量和恢复过程中引起的不确定性，其中使用符合性预测构建了一个区间，并保证以用户指定的概率包含真实图像的任务输出，并使用该区间的宽度来量化由测量和恢复产生的不确定性，我们还提出了一种在多轮测量中停止，直到任务的不确定性降至可接受水平的方法，该方法在加速磁共振成像 (MRI) 上进行了验证。