Abstract
We present statements and a method of solution to the inverse scattering problem of reconstructing permittivity of a dielectric inclusion in a 2D or 3D waveguide from the transmission characteristics. The approach employs a volume singular integral equation (VSIE) method. The unique solvability of VSIE is established. The inverse problem is solved by the method of iterations applied to VSIE; the convergence of the method is proved
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