This topic is explored in the context of Fabien Momey's PhD thesis. The goal is to exploit the inverse approach for image reconstruction in X-ray dynamic tomography.


Dynamic Tomography is a major challenge in radiotherapy

Computerized tomography (CT) aims at the retrieval of 3-D information from a set of projections acquired at different angles around the object of interest. One of its most common applications is X-ray Computerized Tomography medical imaging. This reconstruction can be severely impaired by the patient's breath (respiratory) motion and cardiac beating. The field of methods dealing with the reconstruction of a dynamic sequence of the object of interest is called Dynamic Computerized Tomography. This is a major challenge in radiotherapy, where the precise localization of the tumor is a prerequisite for cancer cells irradiation with preservation of surrounding healthy tissues.

Dynamic reconstruction from a single dataset without motion compensation

Some state-of-the-art methods increase the number of projections, allowing an independent reconstruction of several phases of the time sampled sequence. Other methods use motion compensation in the reconstruction, by a beforehand estimation on a previous data set, getting the explicit motion through a deformation model.

Légende de l'album photo

Our work takes a different path; it uses dynamic reconstruction, based on inverse problems theory, without any additional information, nor explicit knowledge of the motion. The dynamic sequence is reconstructed out of a single data set, only assuming the motion's continuity and periodicity.

This inverse problem is considered as a minimization of an error term combined with a regularization. One of the most original features of the Ph.D. thesis, typical of dynamic CT, is the elaboration of a reconstruction method from very sparse data, using Total Variation (TV) as a very efficient regularization term. We also implement a new rigorously defined and computationally efficient tomographic projector, based on B-splines separable functions, outperforming usual reconstruction quality in a data sparsity context. This reconstruction method is then inserted into a coherent dynamic reconstruction scheme, applying an efficient spatio-temporal TV regularization. Our method exploits current data information only, in an optimal way; moreover, its implementation is rather straightforward.


Our results

We first demonstrate the strength of our approach on 2-D+t reconstructions from numerically simulated dynamic data (cf. Fig. 4).

Then the practical feasibility of our method is established on 2-D and 3-D+t reconstructions of a mechanical phantom and real patient data (cf. Fig. 5).

Fig. 4: Dynamic tomography reconstruction from mechanical phantom data. Fig. 5: Dynamic tomography reconstruction from medical data.



A B-spline based and computationally performant projector for iterative reconstruction in tomography, application to dynamic X-ray gated CT, in 2nd X-ray CT meeting 2012: The Second International Conference on Image Formation in X-Ray Computed Tomography, Momey, F., L. Denis, C. Mennessier, É. Thiébaut, J.-M. Becker & L. Desbat, 2012, Salt Lake City (Utah, juin 2012; Momey_et_al-2012-SaltLakeCity.pdf)