title: Variational Phase Imaging Using the Transport-of-Intensity Equation.
abstract: We 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.
authors.forename: Emrah
authors.initials: E
authors.lastname: Bostan
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Froustey
authors.forename: Masih
authors.initials: M
authors.lastname: Nilchian
authors.forename: Daniel
authors.initials: D
authors.lastname: Sage
authors.forename: Michael
authors.initials: M
authors.lastname: Unser
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006367:HeLa Cells; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008853:Microscopy / Q000379:methods*; D008962:Models, Theoretical