3,062 research outputs found
Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography
Optical diffraction tomography relies on solving an inverse scattering
problem governed by the wave equation. Classical reconstruction algorithms are
based on linear approximations of the forward model (Born or Rytov), which
limits their applicability to thin samples with low refractive-index contrasts.
More recent works have shown the benefit of adopting nonlinear models. They
account for multiple scattering and reflections, improving the quality of
reconstruction. To reduce the complexity and memory requirements of these
methods, we derive an explicit formula for the Jacobian matrix of the nonlinear
Lippmann-Schwinger model which lends itself to an efficient evaluation of the
gradient of the data- fidelity term. This allows us to deploy efficient methods
to solve the corresponding inverse problem subject to sparsity constraints
3D microwave tomography with huber regularization applied to realistic numerical breast phantoms
Quantitative active microwave imaging for breast cancer screening and therapy monitoring applications requires adequate reconstruction algorithms, in particular with regard to the nonlinearity and ill-posedness of the inverse problem. We employ a fully vectorial three-dimensional nonlinear inversion algorithm for reconstructing complex permittivity profiles from multi-view single-frequency scattered field data, which is based on a Gauss-Newton optimization of a regularized cost function. We tested it before with various types of regularizing functions for piecewise-constant objects from Institut Fresnel and with a quadratic smoothing function for a realistic numerical breast phantom. In the present paper we adopt a cost function that includes a Huber function in its regularization term, relying on a Markov Random Field approach. The Huber function favors spatial smoothing within homogeneous regions while preserving discontinuities between contrasted tissues. We illustrate the technique with 3D reconstructions from synthetic data at 2GHz for realistic numerical breast phantoms from the University of Wisconsin-Madison UWCEM online repository: we compare Huber regularization with a multiplicative smoothing regularization and show reconstructions for various positions of a tumor, for multiple tumors and for different tumor sizes, from a sparse and from a denser data configuration
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