*Article* **Dynamic Tomographic Reconstruction of Deforming Volumes**

#### **Clément Jailin \* and Stéphane Roux**

LMT (ENS Paris-Saclay/CNRS/University Paris-Saclay), 61 avenue du Président Wilson, F-94235Cachan,France;stephane.roux@ens-paris-saclay.fr

 **\*** Correspondence: clement.jailin@ens-paris-saclay.fr

Received: 17 July 2018; Accepted: 6 August 2018; Published: 9 August 2018

**Abstract:** The motion of a sample while being scanned in a tomograph prevents its proper volume reconstruction. In the present study, a procedure is proposed that aims at estimating both the kinematics of the sample and its standard 3D imaging from a standard acquisition protocol (no more projection than for a rigid specimen). The proposed procedure is a staggered two-step algorithm where the volume is first reconstructed using a "Dynamic Reconstruction" technique, a variant of Algebraic Reconstruction Technique (ART) compensating for a "frozen" determination of the motion, followed by a Projection-based Digital Volume Correlation (P-DVC) algorithm that estimates the space/time displacement field, with a "frozen" microstructure and shape of the sample. Additionally, this procedure is combined with a multi-scale approach that is essential for a proper separation between motion and microstructure. A proof-of-concept of the validity and performance of this approach is proposed based on two virtual examples. The studied cases involve a small number of projections, large strains, up to 25%, and noise.

**Keywords:** tomographic reconstruction; dynamic tomography; motion compensation; projection-based digital volume correlation
