利用后向近场散射数据成像的Newton－Kantorovich方法研究

An Investigation of Newton-Kantorovich Method for Shape Imaging of Conducting Object Using Near Field Backscattering Data

本文利用多频多入射方向的Ｎｅｗｔｏｎ－Ｋａｎｔｏｒｏｖｉｃｈ方法，结合矩量法求解利用后向近场散射数据，对二维导体目标外形成像而产生的非线性耦合积分方程，然后采用基于Ｇｒａｍ－Ｓｃｈｅｄｍｉｔ正交化的伪逆技术求解所得的病态线性方程组，利用最小二乘法给出迭代的初值。为减小计算量，当迭代到一定程度时，改用修正的Ｎｅｗｔｏｎ－Ｋａｎｔｏｒｏｖｉｃｈ方法，同时，每迭代三次，采用一次加速收敛公式。最后，以数值结果证明了本方法的有效性及抗噪声性能。

Newton-Kantorovich method combined with moment method is applied to solve the nonlinear coulped integral equations arising from imaging of conducting object illuminated by plane waves with multiple frequencies and multiple incident directions in the paper, pseudoinverse technique based on Gram-Schedmit procedure is adopted for the solution of ill-conditioned linear equations. Least square error method(LSE) is adopted to calculate the initial values. Two techniques are also introduced to reduce the CPU time. Numerical results have shown the validity of the method and high tolerance of noise.