中文摘要：

改进拉格朗日（Lagrange）乘子算法为一种二维时域微波断层成像方法,用于检测早期乳腺肿瘤。该方法首先将成像逆问题表示为最优化问题;其次,应用泛函分析和变分法,导出闭式的目标泛函关于电参数的Fréchet导数;最后,借助Polak-Ribière-Polyak（PRP）共轭梯度（CG）法和时域有限差分（FDTD）法迭代求解。为了抑制噪声和伪像,采用了吉洪诺夫（Tikhonov）正则化方案。数值算例中,对二维乳房模型进行了计算,仿真结果显示了该方法的有效性。

英文摘要：

A two-dimensional（2-D） time-domain microwave tomography imaging technique is modified from the Lagrange multipliers method for detection of early-stage breast tumors.At first,this approach formulates the inverse imaging problem as an optimization problem.Next,the closed Fréchet derivatives of the resulting cost functional with respect to the electrical properties are derived based on the functional analysis and variation methods.Finally,we solve iteratively the resulting problem using Polak-Ribière-Polyak（PRP） conjugate gradient（CG） algorithm and the finite-difference time-domain（FDTD） method.Also,the Tikhonov＇s regularization scheme is adopted to suppress noise and clutter.In a numerical example,the presented technique is applied to a 2-D breast model,and results demonstrate its effectiveness.