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Weakly convex discontinuity adaptive regularization for 3D quantitative microwave tomography

Funing Bai (UGent) , Aleksandra Pizurica (UGent) , Bart Truyen, Wilfried Philips (UGent) and Ann Franchois (UGent)
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FWO microwave tomography
Abstract
We present an analysis of weakly convex discontinuity adaptive (WCDA) models for regularizing three-dimensional (3D) quantitative microwave imaging. In particular, we are concerned with complex permittivity reconstructions from sparse measurements such that the reconstruction process is significantly accelerated. When dealing with such a highly underdetermined problem, it is crucial to employ regularization, relying in this case on prior knowledge about the structural properties of the underlying permittivity profile: we consider piecewise homogeneous objects. We present a numerical study on the choice of the potential function parameter for the Huber function and for two selected WCDA functions, one of which (the Leclerc-Cauchy-Lorentzian function) is designed to be more edge-preserving than the other (the Leclerc-Huber function). We evaluate the effect of reducing the number of (simulated) scattered field data on the reconstruction quality. Furthermore, reconstructions from subsampled single-frequency experimental data from the 3D Fresnel database illustrate the effectiveness of WCDA regularization.
Keywords
RESTORATION, microwave imaging, CONSTRAINT, RECONSTRUCTION, ELECTROMAGNETIC INVERSE SCATTERING, electromagnetic scattering, inverse problem, discontinuity adaptive regularization

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Citation

Please use this url to cite or link to this publication:

Chicago
Bai, Funing, Aleksandra Pizurica, Bart Truyen, Wilfried Philips, and Ann Franchois. 2014. “Weakly Convex Discontinuity Adaptive Regularization for 3D Quantitative Microwave Tomography.” Inverse Problems 30 (8).
APA
Bai, F., Pizurica, A., Truyen, B., Philips, W., & Franchois, A. (2014). Weakly convex discontinuity adaptive regularization for 3D quantitative microwave tomography. INVERSE PROBLEMS, 30(8).
Vancouver
1.
Bai F, Pizurica A, Truyen B, Philips W, Franchois A. Weakly convex discontinuity adaptive regularization for 3D quantitative microwave tomography. INVERSE PROBLEMS. 2014;30(8).
MLA
Bai, Funing, Aleksandra Pizurica, Bart Truyen, et al. “Weakly Convex Discontinuity Adaptive Regularization for 3D Quantitative Microwave Tomography.” INVERSE PROBLEMS 30.8 (2014): n. pag. Print.
@article{4144695,
  abstract     = {We present an analysis of weakly convex discontinuity adaptive (WCDA) models for regularizing three-dimensional (3D) quantitative microwave imaging. In particular, we are concerned with complex permittivity reconstructions from sparse measurements such that the reconstruction process is significantly accelerated. When dealing with such a highly underdetermined problem, it is crucial to employ regularization, relying in this case on prior knowledge about the structural properties of the underlying permittivity profile: we consider piecewise homogeneous objects. We present a numerical study on the choice of the potential function parameter for the Huber function and for two selected WCDA functions, one of which (the Leclerc-Cauchy-Lorentzian function) is designed to be more edge-preserving than the other (the Leclerc-Huber function). We evaluate the effect of reducing the number of (simulated) scattered field data on the reconstruction quality. Furthermore, reconstructions from subsampled single-frequency experimental data from the 3D Fresnel database illustrate the effectiveness of WCDA regularization.},
  articleno    = {085005},
  author       = {Bai, Funing and Pizurica, Aleksandra and Truyen, Bart and Philips, Wilfried and Franchois, Ann},
  issn         = {0266-5611},
  journal      = {INVERSE PROBLEMS},
  language     = {eng},
  number       = {8},
  title        = {Weakly convex discontinuity adaptive regularization for 3D quantitative microwave tomography},
  url          = {http://dx.doi.org/10.1088/0266-5611/30/8/085005},
  volume       = {30},
  year         = {2014},
}

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