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We consider the inverse scattering problem of determining the shape of an impenetrable two-dimensional obstacle with a generalized impedance boundary condition from near-field measurements. We propose the reverse time migration method where the imaging functional is defined as the imaginary part of the cross-correlation. Our analysis shows that, on the one hand, the imaging functional has contrast at the boundary of the scatterer and decays outside the scatterer; On the other hand, the imaging functional is always positive thus may have better stability properties. These imply that the approach has powerful imaging quality which is confirmed in our numerical experiments.

Reverse time migration for inverse obstacle scattering with a generalized impedance boundary condition