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3D microwave tomography with huber regularization applied to realistic numerical breast phantoms

Funing Bai (UGent) , Ann Franchois (UGent) and Aleksandra Pizurica (UGent)
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Abstract
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.
Keywords
GAUSS-NEWTON METHOD, ELECTROMAGNETIC INVERSE SCATTERING, TIME-DOMAIN, CANCER DETECTION, DIELECTRIC-PROPERTIES, IMAGE-RECONSTRUCTION, BAYESIAN-APPROACH, ALGORITHM, PROTOTYPE, TISSUES

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Chicago
Bai, Funing, Ann Franchois, and Aleksandra Pizurica. 2016. “3D Microwave Tomography with Huber Regularization Applied to Realistic Numerical Breast Phantoms.” Progress in Electromagnetics Research-pier 155: 75–91.
APA
Bai, F., Franchois, A., & Pizurica, A. (2016). 3D microwave tomography with huber regularization applied to realistic numerical breast phantoms. PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER, 155, 75–91.
Vancouver
1.
Bai F, Franchois A, Pizurica A. 3D microwave tomography with huber regularization applied to realistic numerical breast phantoms. PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER. 2016;155:75–91.
MLA
Bai, Funing, Ann Franchois, and Aleksandra Pizurica. “3D Microwave Tomography with Huber Regularization Applied to Realistic Numerical Breast Phantoms.” PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER 155 (2016): 75–91. Print.
@article{7177745,
  abstract     = {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.},
  author       = {Bai, Funing and Franchois, Ann and Pizurica, Aleksandra},
  issn         = {1559-8985},
  journal      = {PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER},
  keywords     = {GAUSS-NEWTON METHOD,ELECTROMAGNETIC INVERSE SCATTERING,TIME-DOMAIN,CANCER DETECTION,DIELECTRIC-PROPERTIES,IMAGE-RECONSTRUCTION,BAYESIAN-APPROACH,ALGORITHM,PROTOTYPE,TISSUES},
  language     = {eng},
  pages        = {75--91},
  title        = {3D microwave tomography with huber regularization applied to realistic numerical breast phantoms},
  url          = {http://dx.doi.org/10.2528/PIER15121703},
  volume       = {155},
  year         = {2016},
}

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