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An algorithm for the solution of a nonlinear inverse scattering problem in polar coordinates in ultrasonic tomography is presented. The scattering and diffraction of ultrasonic waves propagating through an inhomogeneous, nondispersive medium, f, may be described by the nonlinear integral equation The unknown f is to be determined from measurements of the scattered field u8 = u – ui on ?D Since k = (k, ?) contains information on frequency and direction of propagation of the incident wave both multiple frequencies and multiple angles of incidence information are used in measurements of the scattered field. These integral equations, which are given in two-dimensional rectangular coordinates, are converted to polar coordinates. Then they are written as a nonlinear operator equation T'(w) = 0 which is solved using Newton's method, with the derivative of the operator being the Frchet derivative I!W). The linear operator equations in each step of Newton's method are solved numerically by using piecewise linear function approximations and then solving the resulting linear discrete equations.
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