Level set regularization for nonlinear absorption and phase retrieval in X-ray phase contrast tomography

The in-line X-ray phase contrast imaging technique relies on the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. The simultaneous recovery of the phase and of the absorption is an ill-posed nonlinear inverse problem. If the object is made up of several homogeneous materials, the absorption and the phase are proportional in each material. In this work, in order to include this a priori information, level set regularization methods are used to retrieve the two quantities. The algorithms are evaluated using simulated noisy data. Large decrease of the reconstruction errors is obtained.