  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.
