A study on the orthogonality sampling method corresponding to the observation directions configuration

Abstract

Several theoretical and experimental studies have found that the orthogonality sampling method (OSM) is an effective, simple, and stable non-iterative technique for identifying the location of a set of well-separated small inhomogeneities in inverse scattering problems. However, most studies have been conducted assuming a uniform arrangement of the observation directions and a sufficiently large total number of such directions. The effect of the total number and the arrangement of the observation directions has not been studied. Therefore, this study investigates the effect of the configuration of the observation direction to identify the location of small inhomogeneities using OSM for the first time. We examine this interpretation using the mathematical structure that the indicator function of OSM can be expressed as an infinite series of the Bessel function of integer order and configuration of observation directions. We also demonstrate various simulation results with noisy data to support the constructed interpretation.