BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Variational Phase Imaging Using the Transport-of-Intensity Equation

E. Bostan, E. Froustey, M. Nilchian, D. Sage, M. Unser

IEEE Transactions on Image Processing, vol. 25, no. 2, pp. 807–817, February 2016.

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. 

@ARTICLE(http://bigwww.epfl.ch/publications/bostan1601.html,
AUTHOR="Bostan, E. and Froustey, E. and Nilchian, M. and Sage, D. and
	Unser, M.",
TITLE="Variational Phase Imaging Using the Transport-of-Intensity
	Equation",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2016",
volume="25",
number="2",
pages="807--817",
month="February",
note="")

© 2016 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.