A novel study on the orthogonality sampling method in microwave imaging without background information

Abstract

Orthogonality sampling method (OSM) is a promising non-iterative technique for identifying small anomalies in microwave imaging. For a successful application, complete and accurate values of permittivity and conductivity of the background must be known. If one of values is unknown, inaccurate location and shape of anomaly will be retrieved by using the OSM. This phenomenon was examined through the simulation results but relevant theoretical result has not been established. Motivated by this, we investigate the structure of the indicator function of the OSM by establishing a relationship with an infinite series of the Bessel functions of integer order and applied values of permittivity, permeability, and conductivity. Revealed structure explains the theoretical reason why inaccurate location and shape of anomaly is retrieved through the OSM with inaccurate values of permittivity and conductivity. Various results of numerical simulations with synthetic data are illustrated to support the theoretical result.