A new method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium

A new method is presented for solving the inverse scattering problem of determining the speed of sound in an inhomogeneous medium from the far-field data. If F (a; k , 6 ) are the far-field data corresponding to an incident plane wave with wavenumber k moving in the direction & and F j , ( f ; k , &) are the far-field data for a ball no containing the inhomogeneous region and satisfying an impedance boundary condition on dRo, then this new method is based on determining a function g E L2(aQ), where aQ is the unit sphere, such that L * [ F ( t ; k , & ) -Fj.(t;k,&)]g(P)ds(f) = 1. This approach eliminates the problem of transmission eigenvalues that was inherent in our previous work on this problem.