On the identification of small anomaly in microwave imaging without homogeneous background information

For a successful application of subspace migration algorithm to retrieve the exact location and shape of small anomaly in microwave imaging, one must begin the reconstruction process under the assumption that complete information about the homogeneous background medium, such as background permittivity and conductivity, is available. In many studies, the statistical value of the background medium was adopted, raising the possibility of an incorrect value being applied. Thus, simulation results have been examined in order to identify cases in which an inaccurate location and shape of anomaly were retrieved. However, the theory explaining this phenomenon has not been investigated. In this paper, we apply an alternative wavenumber instead of the true one and identify the mathematical structure of the subspace migration imaging function for retrieving two-dimensional small anomaly by establishing a relationship with an infinite series of Bessel functions of the first kind. The revealed structure explains the reason behind the retrieval of an inaccurate location and shape of anomaly. The simulation results with synthetic data are presented to support the theoretical result.