Model-based deep learning solutions to inverse problems have attracted increasing attention in recent years as they bridge state-of-the-art numerical performance with interpretability. In addition, the incorporated prior domain knowledge can make the training more efficient as the smaller number of parameters allows the training step to be executed with smaller datasets. Algorithm unrolling schemes stand out among these model-based learning techniques. Despite their rapid advancement and their close connection to traditional high-dimensional statistical methods, they lack certainty estimates and a theory for uncertainty quantification is still elusive. This work provides a step towards closing this gap proposing a rigorous way to obtain confidence intervals for the LISTA estimator.

翻译：基于模型的深度学习反问题求解方法近年来备受关注，因其在实现先进数值性能的同时兼具可解释性。此外，融入的先验领域知识可通过更少的参数使训练过程在更小数据集上高效执行。算法展开方案在这些基于模型的学习技术中尤为突出。尽管此类方法发展迅速且与传统高维统计方法密切相关，但其仍缺乏置信度估计，且不确定性量化理论尚不完善。本文通过提出一种严谨方法为LISTA估计器构建置信区间，向弥合这一理论空白迈出关键一步。