  The aim of this article is to elaborate and rigorously analyze a topological
derivative based imaging framework for locating an electromagnetic inclusion of
diminishing size from boundary measurements of the tangential component of
scattered magnetic field at a fixed frequency. The inverse problem of inclusion
detection is formulated as an optimization problem in terms of a filtered
discrepancy functional and the topological derivative based imaging functional
obtained therefrom. The sensitivity and resolution analysis of the imaging
functional is rigorously performed. It is substantiated that the Rayleigh
resolution limit is achieved. Further, the stability of the reconstruction with
respect to measurement and medium noises is investigated and the
signal-to-noise ratio is evaluated in terms of the imaginary part of free space
fundamental magnetic solution.
