When topological derivatives met regularized Gauss-Newton iterations in holographic 3D imaging



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Carpio, Ana and Dimiduk, Thomas G. and Le Louër, Frédérique and Rapún, María Luisa (2019) When topological derivatives met regularized Gauss-Newton iterations in holographic 3D imaging. Journal of Computational Physics, 388 . pp. 224-251. ISSN 00219991

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Official URL: https://doi.org/10.1016/j.jcp.2019.03.027


We propose an automatic algorithm for 3D inverse electromagnetic scattering based on the combination of topological derivatives and regularized Gauss-Newton iterations. The algorithm is adapted to decoding digital holograms. A hologram is a two-dimensional light interference pattern that encodes information about three-dimensional shapes and their optical properties. The formation of the hologram is modeled using Maxwell theory for light scattering by particles. We then seek shapes optimizing error functionals which measure the deviation from the recorded holograms. Their topological derivatives provide initial guesses of the objects. Next, we correct these predictions by regularized Gauss-Newton techniques devised to solve the inverse holography problem. In contrast to standard Gauss-Newton methods, in our implementation the number of objects can be automatically updated during the iterative procedure by new topological derivative computations. We show that the combined use of topological derivative based optimization and iteratively regularized Gauss-Newton methods produces fast and accurate descriptions of the geometry of objects formed by multiple components with nanoscale resolution, even for a small number of detectors and non convex components aligned in the incidence direction.

Item Type:Article
Uncontrolled Keywords:Three-dimensional sensing, Inverse problems, Inverse electromagnetic scattering, Optimization, Topological derivatives, Iteratively regularized Gauss-Newton methods
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Mathematics > Operations research
Sciences > Mathematics > Topology
ID Code:55541
Deposited On:31 May 2019 16:58
Last Modified:10 Jan 2022 18:51

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