本文提出了一种基于对比源的微波成像矩阵算法。目前常用的微波成像算法主要采用迭代求解的这一模式，例如传统的对比源反演采用梯度优化的方法进行迭代运算，随机优化算法在构建目标函数的基础上进行迭代求解。但是迭代求解的时间成本与硬件成本非常高，并且针对复杂成像问题易产生较大误差。本文首先对传统成像模型进行改进，为保证对比源的恒定，采用固定位置的激励源入射，在多层圆周上均匀分布的测量点接收散射信号。其次从Lippman-Schwinger方程出发推导了矩阵算法的物理模型，最后采用多种相对介电常数分布的成像问题，对算法进行了验证。仿真结果表明，本文提出的微波成像矩阵算法计算效率高，并且针对复杂成像问题具有良好的性能。

A microwave imaging matrix algorithm based on contrast source is proposed in this paper. Currently commonly utilized microwave imaging algorithms mainly adopt iterative solution. For instance, traditional contrast source inversion employs gradient optimization method for iterative operation, and stochastic optimization algorithm performs iterative solution based on the construction of the objective function. However, the time cost and hardware cost of iterative solution are very high, and large errors are likely to be obtained for complex imaging problems. This paper first improves the model of traditional imaging that a fixed excitation source for incident is applied and several receivers on the multi-layer uniform circle are applied to obtain scattering signal to ensure the constancy of the contrast source. Secondly, the physical model of the matrix algorithm is deduced from Lippman-Schwinger equation. Finally, a variety of imaging problems of relative permittivity distribution are employed to verify the algorithm performance. The simulation results show that the microwave imaging matrix algorithm proposed in this paper has high computational efficiency and good performance for complex imaging problems.