  Current state-of-the-art motion-based dynamic computed tomography
reconstruction techniques estimate the deformation by considering motion models
in the entire object volume although occasionally the proper change is local.
In this article, we address this issue by introducing the region-based
Motion-compensated Iterative Reconstruction Technique (rMIRT). It aims to
accurately reconstruct the object being locally deformed during the scan, while
identifying the deformed regions consistently with the motion models. Moreover,
the motion parameters that correspond to the deformation in those areas are
also estimated. In order to achieve these goals, we consider a mathematical
optimization problem whose objective function depends on the reconstruction,
the deformed regions and the motion parameters. The derivatives towards all of
them are formulated analytically, which allows for efficient reconstruction
using gradient-based optimizers. To the best of our knowledge, this is the
first iterative reconstruction method in dynamic CT that exploits the
analytical derivative towards the deformed regions.
