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This paper discusses the problem of choosing an appropriate direction of the test dipole used in linear sampling for the 2-dimensional inverse scattering problem of the transverse electric case. In particular, we propose two approaches, one purely mathematical and the other based on the physics theory of multipole expansion of the scattered magnetic field. It is shown that though the approaches are drawn from different perspectives, they perform similarly and show reasonable reconstruction for several interesting and difficult to reconstruct dielectric scatterers.

TEST DIPOLE SELECTION FOR LINEAR SAMPLING IN TRANSVERSE ELECTRIC CASE