We consider the application of a subspace migration (SM) algorithm to quickly identify small objects in microwave imaging. In various problems, it is easy to measure the diagonal elements of the scattering matrix if the location of the transmitter and the receiver is the same. To address this issue, several studies have been conducted by setting the diagonal elements to zero. In this paper, we generalize the imaging problem by setting diagonal elements of the scattering matrix as a constant with the application of SM. To show the applicability of SM and its dependence on the constant, we show that the imaging function of SM can be represented in terms of an infinite series of the Bessel functions of integer order, antenna number and arrangement, and applied constant. This result enables us to discover some further properties, including the unique determination of objects. We also demonstrated simulation results with synthetic data to support the theoretical result.

翻译：本文考虑应用子空间迁移（SM）算法快速识别微波成像中的小目标。在许多问题中，若发射器与接收器位置相同，则散射矩阵的对角元素易于测量。为解决此问题，现有研究通常将对角元素设为零。本文通过将散射矩阵对角元素设为常数，并结合SM算法推广此类成像问题。为证明SM的适用性及其对常数的依赖性，我们证明SM的成像函数可表示为整数阶贝塞尔函数、天线数量和排列方式以及应用常数的无穷级数形式。该结果使我们能够发现若干性质，包括目标的唯一确定性。同时，我们通过合成数据的仿真结果验证理论结论。