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

Publisher Website
Google Scholar
Abstract
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(x; k, alpha ) are the far-field data corresponding to an incident plane wave with wavenumber k moving in the direction alpha and Flambda (x; k, alpha ) are the far-field data for a ball Omega 0 containing the inhomogeneous region and satisfying an impedance boundary condition on delta Omega 0, then this new method is based on determining a function g in L2( delta Omega ), where delta Omega is the unit sphere. This approach eliminates the problem of transmission eigenvalues that was inherent in the authors' previous work on this problem.