Digital phase reconstruction via iterative solutions of transport-of-intensity equation

We develop a variational algorithm for reconstructing phase objects from a series of bright field micrographs. Our mathematical model is based on the transport-of-intensity equation (TIE), which links the phase of a complex field to the axial derivative of its intensity. To reduce reconstruction artifacts, we formulate TIE in a regularized fashion by introducing a family of penalty functionals based on the eigenvalues of the structure tensor. To solve the arising optimization problem, we propose an algorithm based on the alternating direction method of multipliers (ADMM). We apply our method on simulated data and illustrate improved performance compared to the conventional methods such as Tikhonov and total variation (TV) regularizations. We further demonstrate the applicability of the proposed approach by applying it to experimentally-acquired bright field data.