Bostan, E.Froustey, E.Nilchian, M.Sage, D.Unser, M.2016-02-242016-02-242016-02-24201610.1109/TIP.2015.2509249https://infoscience.epfl.ch/handle/20.500.14299/124382WOS:000383905800024We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies—depending on the defocus value of the measurements—in a regularized fashion. The minimization task is solved iteratively via the alternating-direction method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy data of HeLa cells.Phase retrievaltransport-of-intensity equationsparse reconstructiontotal variation regularizationweighted-norm regularizationphase imagingphase microscopetext::journal::journal article::research article