Time-Domain Electromagnetic Inversion Technique for Biological Tissues by Reconstructing Distributions of Cole-Cole Model Parameters
关键词:
Biological tissues, conjugate gradient methods, electromagnetic scattering by dispersive media, electromagnetic scattering inverse problems, finitedifference time-domain (FDTD) methods, regulators摘要
The Cole-Cole (C-C) models have been frequently used for a precise description of the dispersion characteristics of biological tissues. One of the main difficulties in the direct reconstruction of these dielectric properties from time-domain measurements is their frequency dependence. In order to overcome this difficulty, an electromagnetic (EM) inversion technique in the time domain is proposed, in which four kinds of frequency-independence model parameters, the optical relative permittivity, the static conductivity, the relative permittivity difference, and the relaxation time, can be determined simultaneously. It formulates the inversion problem as a regularized minimization problem, whose forward and backward subproblems could be solved iteratively by the finite-difference time-domain (FDTD) method and any conjugate gradient algorithm, respectively. Numerical results on two types of stratified C-C slabs, with smooth and discontinuous parameter profiles, respectively, confirm the performance of the inversion methodology.
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参考
T. G. Papadopoulos and I. T. Rekanos, “Estimation of the parameters of Lorentz dispersive media using a time-domain inverse scattering technique,” IEEE Trans. Magn., vol. 48, no. 2, pp. 219-222, Feb. 2012.
F. Bai, A. Franchois, and A. Pizurica, “3D microwave tomography with Huber regularization applied to realistic numerical breast phantoms,” Progress In Electromagnetics Research, vol. 155, pp. 75-91, 2016.
M. T. Bevacqua and R. Scapaticci, “A compressive sensing approach for 3D breast cancer microwave imaging with magnetic nanoparticles as contrast agent,” IEEE Trans. Med. Imag., vol. 35, no. 2, pp. 665-673, Feb. 2016.
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory. Berlin: Springer-Verlag, 1992.
W. Zhang and Q. H. Liu, “Three-dimensional scattering and inverse scattering from objects with simultaneous permittivity and permeability contrasts,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 1, pp. 429-439, Jan. 2015.
T. G. Papadopoulos and I. T. Rekanos, “Timedomain microwave imaging of inhomogeneous Debye dispersive scatterers,” IEEE Trans. Antennas Propagat., vol. 60, no. 2, pp. 1197-1202, Feb. 2012.
I. T. Rekanos and A. Räisänen, “Microwave imaging in the time domain of buried multiple scatterers by using an FDTD-based optimization technique,” IEEE Trans. Magn., vol. 39, no. 3, pp. 1381-1384, May 2003.
T. Takenaka, H. Jia, and T. Tanaka, “Microwave imaging of electrical property distributions by a forward-backward time-stepping method,” J. Electromagn. Waves Appl., vol. 14, no. 12, pp. 1609-1626, 2000.
I. T. Rekanos, “Time-domain inverse scattering using Lagrange multipliers: An iterative FDTDbased optimization technique,” J. Electromagn. Waves Appl., vol. 17, no. 2, pp. 271-289, 2003.
S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues. III. Parametric models for the dielectric spectrum of tissues,” Phys. Med. Biol., vol. 41, no. 11, pp. 2271-2293, Nov. 1996.
D. W. Winters, E. J. Bond, B. D. V. Veen, and S. C. Hagness, “Estimation of frequency-dependent average dielectric properties of breast tissue using a time-domain inverse scattering technique,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3517- 3528, Nov. 2006.
I. T. Rekanos and T. G. Papadopoulos, “An auxiliary differential equation method for FDTD modeling of wave propagation in Cole-Cole dispersive media,” IEEE Trans. Antennas Propag., vol. 58, no. 11, pp. 3666-3674, Nov. 2010.
I. T. Rekanos and T. V. Yioultsis, “Approximation of Grünwald-Letnikov fractional derivative for FDTD modeling of Cole-Cole media,” IEEE Trans. Magn., vol. 50, no. 2, pp. 7004304, Feb. 2014.
H. Sagan, Introduction to the Calculus of Variations. New York, NY: McGraw-Hill, 1969.
M. Dalir and M. Bashour, “Applications of fractional calculus,” Applied Mathematical Sciences, vol. 4, no. 21, pp. 1021-1032, 2010.
Y. H. Dai, “A family of hybrid conjugate gradient methods for unconstrained optimization,” Math. Comput., vol. 72, no. 243, pp. 1317-1328, Feb. 2003.
J. A. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett., vol. 27, no. 5, pp. 334-339, Dec. 2000.
W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,” IEEE Microw. Guided Wave Lett., vol. 5, no. 12, pp. 439-441, Dec. 1995.
Q. Fang, P. M. Meaney, and K. D. Paulsen, “Microwave image reconstruction of tissue property dispersion characteristics utilizing multiple-frequency information,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1866- 1875, Aug. 2004.
P. R. Johnston and R. M. Gulrajani, “Selecting the corner in the L-curve approach to Tikhonov regularization,” IEEE Trans. Biomed. Eng., vol. 47, no. 9, pp. 1293-1296, Sep. 2000.
L. Hao and L. Xu, “Joint L1 and total variation regularization for magnetic detection electrical impedance tomography,” ACES Journal, vol. 31, no. 6, June 2016.
