An approach to inverse scattering problems.

There are several reasons for investigating the inverse scattering problem in medical image processing. A typical case, that of ultrasonic fields, is considered. Assuming that a plane wave illuminates a weakly inhomogeneous two-dimensional object, the fundamental equation is derived for the scattered waves in integral as well as in differential forms. It is shown that the scattered waves observed on a circle surrounding the object is sufficient to specify the structure of the object. This information is summarized in a single term, which is a function of the wavenumber as well as the angles of incidence and observations. A successive approximation is applied to reconstruct the image of the object from this function. Since no analytic solution is available, several methods of approximations are proposed, and examples of computations are shown for the case of a cylindrical object.