The numerical solution of an inverse scattering problem for acoustic waves

In a previous paper, the authors presented a dual space methodfor the numerical solution of the two-dimensional inverse scatteringproblem for acoustic waves in an inhomogeneous medium. Here,by making major modifications to the dual space method, a dramaticimprovement in the numerical performance of this method is achievedfor solving the inverse scattering problem.     

Uniqueness Theorems for the Inverse Problem of Acoustic Scattering

Uniqueness theorems are obtained for the problem of determiningthe shape of a sound-soft or sound-hard obstacle from a knowledgeof (1) the far-field pattern at a fixed value of the wave numberand a finite number of distinct incident fields, or (2) thetotal scattering cross section for an interval of wave numbersand the incident field propagating in an arbitrary direction.     

The Inverse Scattering Problem for Time-Harmonic Acoustic Waves in an Inhomogeneous Medium: Numerical Experiments

In this paper, the authors describe a new algorithm for solvingthe inverse scattering problem of determining the speed of soundin an inhomogeneous medium from far-field data. Limited testinghas shown that the algorithm has some capacity for reconstructingsimple sound profiles using data over a limited range of frequencies.