Non-linear phase retrieval combined with iterative thresholding in wavelet coordinates

With hard X-rays synchrotron beams, phase contrast can be obtained with the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. We have studied the resolution of this inverse problem with an iterative thresholding algorithm in wavelet coordinates combined with an iterative nonlinear method with a Tikhonov regularization. The phase retrieval algorithm was tested for a 3D Shepp-Logan phantom in the presence of noise. The results show that the combined approach outperforms the Mixed, the CTF and the nonlinear methods.