Uncertainty quantification for learned ISTA
This work addresses a gap in interpretability and reliability for researchers and practitioners using algorithm unrolling in inverse problems, though it is incremental as it builds on existing LISTA frameworks.
The paper tackles the lack of uncertainty quantification in learned ISTA (LISTA) estimators for inverse problems, proposing a rigorous method to obtain confidence intervals for these model-based deep learning approaches.
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.