A new approach to diffraction tomography

A method for reconstructing the image of a loss-less object from the measurement of its scattering amplitude is developed for the case of acoustic wave scattering from an inhomogeneous medium consisting of velocity fluctuations (Helmholtz equation). The inversion procedure is exact, and explicitly takes into account all orders of multiple scattering. The technique is based on a consideration of the analyticity properties of the scattering amplitude in the complex scattering angle domain and recovers the Laplace domain representation of the speed-of-sound fluctuations from the angle-scattered data. The method has the disadvantage of being dependent on analytic continuation procedures, which are likely be noise sensitive in practice.