Real-time detection of small anomaly from limited-aperture measurements in real-world microwave imaging

Abstract

This study concerns a subspace migration technique used to identify the shape and location of an unknown anomaly from scattered parameter data collected within the scattering matrix for a limited-aperture inverse scattering problem. The mathematical theories of subspace migration are partially understood in terms of limited-aperture inverse scattering problems, but little investigation of real-world applications, such as microwave imaging, has taken place. Hence, we perform further research to analyze the subspace migration and explain the reasons for a number of unexplained phenomena. For theoretical corroboration, we prove that the imaging function of subspace migration is composed of an infinite series of integer-order Bessel functions of the first kind, and we outline the arrangement and the total number of antennas for transmitting and receiving signals. This is based on the application of the Born approximation to the identification of an anomaly and the uniform convergence of the Jacobi–Anger expansion formula. Various results of numerical simulations with synthetic and real data are exhibited to support the theoretical results of the imaging function and explain the reasons for a number of phenomena as well as the fundamental limitations. Further, we suggest a method of antenna arrangement to obtain better results and confirm the improvements through simulations.