Stabilizing the iterative solution to ultrasonic transmission 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 analysis of nonlinear tomography. An implicit conjugate gradient-type iterative formula is used to solve a weighted least-squares problem. In the iterative process, a damping factor of linear increase rather than a constant is used to filter out the influences of smaller singular values' components. The results of simulated data show that our method can efficiently stabilize the iteration, and provide a robust solution.