On the Application of Orthogonality Sampling Method for Object Detection in Microwave Imaging

We consider a further development of the orthogonality sampling method (OSM) for a fast localization of small object in microwave imaging (MI). In contrast to the scenarios considered in traditional approaches, if the location of the transmitter and the receiver is the same, it is very hard to measure the scattering parameter data or to distinguish the weak scattered signal from the relatively high antenna reflection. Here, we set the unknown measurement data as a constant and design an indicator function for the OSM. To demonstrate the applicability of the OSM and its dependence on the constant, we show that the designed indicator function can be represented in terms of an infinite series of the Bessel functions of integer order, antenna configuration, and applied constant. To improve the imaging performance for a proper identification of the object, we design a new indicator function of the OSM with multiple sources, rigorously explore its mathematical structure, and discover some properties including the improvement and uniqueness. Simulation results with synthetic and real data are exhibited to support the theoretical results and to illustrate the pros and cons of the designed OSM.