Phase contrast imaging coupled to tomography is a new imaging modality especially attractive for soft tissue within dense structure but the phase recovery remains an issue.  The quantity reconstructed in this case is related to a projection of the refractive index in the object. If the spatial coherence of the x-rays is sufficient, phase contrast can be achieved by letting the beam propagate in the free space after interaction with the object. The relationship between the phase shift induced by a sample and the intensity recorded at several sample-to-detector distances has been established. It can be used as a basis to set the inverse problem of the phase recovery. Several phase retrieval methods based on the linearization of the forward problem have already been investigated . Yet, the reconstructed phase obtained remains an approximation of the object for hard samples.
The objective of this work is to study various non linear iterative approaches of this phase retrieval problem.
In order to improve the former algorithm, we will study various non linear iterative approaches. These methods are based on the Frechet derivative of the phase intensity relationship I(). The introduction of proper prior information to regularize the problem will particularly be investigated since the inverse problem is ill-posed. The performance of the method in presence of noise will be also discussed. Special attention will also be devoted to computing efficiency due to the large data set to be managed. Our algorithms will be evaluated using both simulated data and real images obtained at the ESRF in Grenoble, with a privileged application on biomaterials for bone tissue engineering.
Compétences requises :
Traitement d’image, méthodes d’optimisation.
Programmation (matlab, C++).
 M.Langer, P.Cloetens, J.P.Guigay, F.Peyrin “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography” Med.Phys.35 (10) 2008 p 4556.