X-ray computed tomography (X-ray CT) is a 3D imaging technique that enables the visualization of the internal microstructure of a specimen in a non-destructive way. Highly developed in a medical context, it is also a standard instrument in research laboratories for studying advanced materials, complex industrial parts, or biological samples. It consists of acquiring a collection of 2D projections (radiographs) while the sample rotates and (computationally) reconstructing the volume absorption in 3D. Such reconstructions require that the sample remains perfectly still during the entire acquisition. In the case of motion, the reconstructed 3D image will become fuzzy and unexploitable when details matter. The goal of the present project, imaging in 3D a moving sample, is a very ambitious challenge, and breaking this limit would open avenues with enhanced time resolution and low-dose exposure. • 3D kinematics can be read from tomographic reconstructions (when available) through volume registration. A measurement method called 3D/2D registration or P-DVC has been developed for medical imaging and material science based on a known reference volume. The latter is warped in space and time so that its projections match those acquired in motion, providing the volume 4D displacement field (3D space + time) during acquisition. • The tomographic reconstruction procedure can be motion-compensated when the 4D displacement field is known. These techniques have been developed based on different reconstruction algorithms. However, in the context of the Ph.D. neither the reference volume nor the displacement field are available. Dynamic reconstruction involves coupling the two previous techniques: motion-compensated reconstruction and kinematic measurement during acquisition. Starting from a first motion initialization, a motion-blurred volume can be reconstructed and used to identify a more precise displacement field relative to its own projections. This field can then update the volume reconstruction and allows through iterations to estimate volume and kinematics. Introducing a mechanical description is key to formulating a reduced model for the kinematics and quantifying it. This approach is vital for mechanical model identification and/or for avoiding unrealistic distortions in the reconstructed image. Another opportunity lies in artificial intelligence methods for processing the reconstructed volume (e.g., machine learning models or neural networks). They offer various advantages, such as denoising the image, clearing out artifacts, and segmenting different phases. They could be integrated into a dynamic algorithm to reduce the necessary measurements further. This integration offers a space and time refinement of the reconstruction, opening up new possibilities in dynamic imaging. This thesis aims to establish dynamic reconstruction methods for imaging ultra-fast phenomena (increasing temporal resolutions by several orders of magnitudes, both in laboratory tomographs and large-scale instruments (synchrotron beamtime is targeted for the PhD). Examples of applications are numerous in material science (phase change in alloys, damage in a porous material, tracking two-phase flows through porous materials, foam expansion, etc.), as well as for medical imaging. The LMPS has a growing expertise in mechanically-informed dynamic reconstruction. A PhD, currently in progress between LMPS and GE HealthCare (Matteo Barbieri, 2022-2025), involves implementing dynamic tomosynthesis methods for Digital Breast Tomosynthesis. It also has strong industrial partners in medical imaging and non-destructive testing who are strongly motivated by these approaches.

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