A Number Of Special Areas Of Uniqueness Of Inverse Scattering And Electrical Conductivity Discontinuity Reconstruction Method

In this paper,we consider two kinds of inverse problems.In the first part,we prove the uniqueness in the inverse acoustic scattering problem within circular and elliptical domains by a single incident wave in the sound-soft case and the sound-hard case.The proof is based on the reflection solution of the Helmholtz equation.In the second part, one level set method for EIT problem is proposed,which can successfully reconstruct the interface of discontinuity of the conductivity.We detailedly introduce the designation of the reconstruction algorithm,the numerical methods of level set equation and the important velocity function.Our reconstruction algorithm is effcient and stable in numerical examples.