Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimization.

State-of-the-art techniques for phase retrieval in propagation based X-ray phase-contrast imaging are aiming to solve an underdetermined linear system of equations. They commonly employ Tikhonov regularization - an L2-norm regularized deconvolution scheme - despite some of its limitations. We present a novel approach to phase retrieval based on Total Variation (TV) minimization. We incorporated TV minimization for deconvolution in phase retrieval using a variety of the most common linear phase-contrast models. The results of our TV minimization was compared with Tikhonov regularized deconvolution on simulated as well as experimental data. The presented method was shown to deliver improved accuracy in reconstructions based on a single distance as well as multiple distance phase-contrast images corrupted by noise and hampered by errors due to nonlinear imaging effects.