Image reconstruction in dynamic inverse problems with temporal models

TL;DR

This paper reviews variational methods for dynamic inverse image reconstruction, focusing on temporal models like diffeomorphic deformations and PDE-based motion constraints, and discusses recent deep learning integrations.

Contribution

It provides a comprehensive survey of variational approaches with temporal models and recent deep learning techniques applied to dynamic inverse problems.

Findings

Methods apply to 2D dynamic tomography

Integration of deep learning enhances computational efficiency

Temporal models improve reconstruction accuracy

Abstract

The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent parameters, or as motion constrained reconstruction where the motion model is given by a partial differential equation. The survey also includes recent development in integrating deep learning for solving these computationally demanding variational methods. Examples are given for 2D dynamic tomography, but methods apply to general inverse problems.