Stabilizing the iterative solution to ultrasonic ray tomography

A stable iterative reconstruction algorithm is presented for ultrasonic tomography through the uses of weighting matrices, damping factor and the features of conjugate gradient method. The weighting matrices are chosen according to Berryman´s (1989) analysis of nonlinear tomography. An explicit conjugate gradient-type iterative formula is derived for solving weighted least-squares problems. In an iterative process, a damping factor of linear increase rather than a constant is used to filter out the influences of singular values components associated with smaller singular values. The results of simulated data show that the authors´ method can efficiently stabilize the iteration, and provide a robust solution