Learned RESESOP for solving inverse problems with inexact forward operator

TL;DR

This paper introduces a learned version of ReSeSOp, an iterative reconstruction method, enabling dynamic inexactness estimation during inverse problem solving, with demonstrated improvements in dynamic imaging applications.

Contribution

It proposes a novel learned ReSeSOp framework that adapts to inexact forward operators in real-time, extending existing unrolled iterative schemes for dynamic imaging.

Findings

Improved reconstruction quality in dynamic imaging tasks.

Effective handling of model inexactness without prior estimates.

Validated on diverse datasets including CT and MRI.

Abstract

When solving inverse problems, one has to deal with numerous potential sources of model inexactnesses, like object motion, calibration errors, or simplified data models. Regularized Sequential Subspace Optimization (ReSeSOp) allows to compensate for such inaccuracies within the reconstruction step by employing consecutive projections onto suitably defined subspaces. However, this approach relies on a priori estimates for the model inexactness levels which are typically unknown. In dynamic imaging applications, where inaccuracies arise from the unpredictable dynamics of the object, these estimates are particularly challenging to determine in advance. To overcome this limitation, we propose a learned version of ReSeSOp which allows to approximate inexactness levels on the fly. The proposed framework generalizes established unrolled iterative reconstruction schemes to inexact forward operators and is particularly tailored to the structure of dynamic problems. We also present a comprehensive mathematical analysis regarding the effect of dependencies within the forward problem, clarifying when and why dividing the overall problem into subproblems is essential. The proposed method is evaluated on various examples from dynamic imaging, including datasets from a rheological CT experiment, brain MRI, and real-time cardiac MRI. The respective results emphasize improvements in reconstruction quality while ensuring adequate data consistency.