Analysis of multi-frequency subspace migration weighted by natural logarithmic function for fast imaging of two-dimensional thin, arc-like electromagnetic inhomogeneities

Abstract: The present study seeks to investigate mathematical structures of a multi-frequency subspace migration weighted by the natural logarithmic function for imaging of thin electromagnetic inhomogeneities from measured far-field pattern. To this end, we designed the algorithm and calculated the indefinite integration of square of Bessel function of order zero of the first kind multiplied by the natural logarithmic function. This is needed for mathematical analysis of improved algorithm to demonstrate the reason why proposed multi-frequency subspace migration contributes to yielding better imaging performance, compared to previously suggested subspace migration algorithm. This analysis is based on the fact that the singular vectors of the collected Multi-Static Response (MSR) matrix whose elements are the measured far-field pattern can be represented as an asymptotic expansion formula in the presence of such inhomogeneities. To support the main research results, several numerical experiments with noisy data are illustrated.