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Phase contrast tomography is an alternative to classic absorption contrasttomography that leads to higher contrast reconstructions in many applications.We review how phase contrast data can be acquired by using a combination ofphase and absorption gratings. Using algebraic reconstruction techniques theobject can be reconstructed from the measured data. In order to solve theresulting linear system we propose the Generalized Bidiagonal Tikhonov (GBiT)method, an adaptation of the generalized Arnoldi-Tikhonov method that uses thebidiagonal decomposition of the matrix instead of the Arnoldi decomposition. Wealso study the effect of the finite difference operator in the model byexamining the reconstructions with either a forward difference or a centraldifference approximation. We validate our conclusions with simulated andexperimental data.

A Generalized Bidiagonal-Tikhonov Method Applied To Differential Phase Contrast Tomography