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针对基于金属腔体的微波断层成像系统，提出了一种最优分层非均一背景的设计方法. 该方法使用一种新的微波断层成像积分算子评价方法和模拟退火法等最优化方法. 首先，介绍了一种基于有限元法的微波断层成像积分算子计算方法. 然后，提出一种新的微波断层成像积分算子度量，该度量可以综合评价整个积分算子奇异值谱，并通过一组仿真研究证明该度量与反演结果的误差具有相关性；该度量用一个数值综合评价一个积分算子，可以方便地应用于最优化算法中；利用模拟退火法选择圆形金属腔体中分层非均一背景的每一层介质的相对介电常数，从而获得一个最优分层非均一背景. 最后，对尺寸小于半波长的圆柱目标和“凹”字形复杂目标进行仿真研究，仿真结果证明该最优分层非均一背景可以提高微波断层成像算法的收敛速度，提高反演结果的准确性.An optimal layered inhomogeneous background which can be used in an embedded microwave tomography system is proposed. The method is based on a new evaluation method of integral radiation operator with respect to an configuration and optimal methods such as simulated annealing method. First, the integral radiation operator is calculated using the finite element method. Then, a kind of metric which can be used to evaluate the operator is proposed. The metric contains information about the whole singular value spectrum of a integral radiation operator. A set of synthetic researches is performed to show the correlation between the metric and inversion error. The method can evaluate an integral radiation operator using a number, and it can be used in optimal process easily as the cost function. Simulated annealing method is employed to obtain the permittivity of each layer in the optimal layered inhomogeneous background. Finally, synthetic researches are employed both on simple target and complex target to test the optimal layered inhomogeneous background. The results show that the optimal layered inhomogeneous background can expedite the convergence process and more accurate inversion results can be obtained.
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Keywords:
- inverse scattering /
- microwave tomography /
- inhomogeneous background /
- optimization
[1] Meaneya P M, Fanninga M W, Raynoldsa T, Foxa C J, Fang Q, Kogelb C A, Poplackb S P, Paulsena K D 2007 Acad. Radiol. 14 207
[2] Zakaria A, Baran A, LoVetri J 2012 IEEE Antennas. Wirel. Propag. Lett. 11 1606
[3] Song L P, Yu C, Liu Q H 2005 IEEE Trans. Geosci. Remote Sens. 43 2793
[4] Abubakar A, Habashy T M, Druskin V L, Knizhnerman L, Alumbaugh D 2008 Geophysics 73 F165
[5] Zhu H Y, Shen J Q, Li J 2004 Acta Phys. Sin. 53 947(in Chinese)[朱红毅, 沈建其, 李军 2004 53 947]
[6] Zhang P, Zhang X J 2013 Acta Phys. Sin. 62 164201(in Chinese)[张鹏, 张晓娟 2013 62 164201]
[7] Sheen D M, McMakin D L, Hall T E 2001 IEEE Trans. Microw. Theory Tech. 49 1581
[8] Wang F F, Zhang Y R 2012 Chin. Phys. B 21 050204
[9] Xiao X, Xu L, Li Q W 2013 Chin. Phys. B 22 094101
[10] Crocco L, Litman A 2009 Inverse Probl. 25 065001
[11] Gilmore C, LoVetri J 2008 Inverse Probl. 24 035008
[12] Williams T C, Sill J M, Fear E C 2008 IEEE Trans. Biomed Eng. 55 1678
[13] Williams T C, Bourqui J, Cameron T R, Okoniewski M, Fear E C 2011 IEEE Trans. Biomed Eng. 58 1193
[14] Ding L, Liu P G, He J G, Zakaria A, LoVetri J 2014 Acta Phys. Sin. 63 044102(in Chinese)[丁亮, 刘培国, 何建国, Amer Zakaria, Joe LoVetri 2014 63 044102]
[15] Zakaria A, Gilmore C, LoVetri J 2010 Inverse Probl. 26 115010
[16] Xie Z B, Feng J C 2011 Chin. Phys. B 20 050504
[17] Mojabi P, LoVetri J 2009 IEEE Antennas. Wirel. Propag. Lett. 8 645
[18] Zakaria A, LoVetri J 2011 IEEE Trans. Antennas Propag. 59 3495
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[1] Meaneya P M, Fanninga M W, Raynoldsa T, Foxa C J, Fang Q, Kogelb C A, Poplackb S P, Paulsena K D 2007 Acad. Radiol. 14 207
[2] Zakaria A, Baran A, LoVetri J 2012 IEEE Antennas. Wirel. Propag. Lett. 11 1606
[3] Song L P, Yu C, Liu Q H 2005 IEEE Trans. Geosci. Remote Sens. 43 2793
[4] Abubakar A, Habashy T M, Druskin V L, Knizhnerman L, Alumbaugh D 2008 Geophysics 73 F165
[5] Zhu H Y, Shen J Q, Li J 2004 Acta Phys. Sin. 53 947(in Chinese)[朱红毅, 沈建其, 李军 2004 53 947]
[6] Zhang P, Zhang X J 2013 Acta Phys. Sin. 62 164201(in Chinese)[张鹏, 张晓娟 2013 62 164201]
[7] Sheen D M, McMakin D L, Hall T E 2001 IEEE Trans. Microw. Theory Tech. 49 1581
[8] Wang F F, Zhang Y R 2012 Chin. Phys. B 21 050204
[9] Xiao X, Xu L, Li Q W 2013 Chin. Phys. B 22 094101
[10] Crocco L, Litman A 2009 Inverse Probl. 25 065001
[11] Gilmore C, LoVetri J 2008 Inverse Probl. 24 035008
[12] Williams T C, Sill J M, Fear E C 2008 IEEE Trans. Biomed Eng. 55 1678
[13] Williams T C, Bourqui J, Cameron T R, Okoniewski M, Fear E C 2011 IEEE Trans. Biomed Eng. 58 1193
[14] Ding L, Liu P G, He J G, Zakaria A, LoVetri J 2014 Acta Phys. Sin. 63 044102(in Chinese)[丁亮, 刘培国, 何建国, Amer Zakaria, Joe LoVetri 2014 63 044102]
[15] Zakaria A, Gilmore C, LoVetri J 2010 Inverse Probl. 26 115010
[16] Xie Z B, Feng J C 2011 Chin. Phys. B 20 050504
[17] Mojabi P, LoVetri J 2009 IEEE Antennas. Wirel. Propag. Lett. 8 645
[18] Zakaria A, LoVetri J 2011 IEEE Trans. Antennas Propag. 59 3495
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