GAUSS-NEWTON METHOD IN REVERSE RECONSTRUCTION PROBLEMS OF COMPUTED TOMOGRAPHY PHANTOM IMAGES

In this paper we study problems in reverse reconstruction of a wave equation with Gauss-Newton method and improve upon it. One of the most prominent engineering and computational science challenges is estimating of large scale, nonlinear parameters in the described systems with PDE (Partial Differential Equation).These problems are called Reverse Problems as opposed to Direct Problems that describe large-scale simulations. Inverse problems are solved with more difficulty compared to direct problems because of many reason including ill-posedness, imperfect conditions of high density operators, coupled space-time and the need to solve direct problems for several times.We present a parallel algorithm for inverse problems described by temporal PDE and results of scalability of an inverse wave propagation problem in determining the material field of an acoustic media. We used total variation regularization, preconditioned matrix-free Gauss-Newton iteration, algorithmic check pointing and multiscale continuation to address the mentioned problems. Finally, we solved a synthetic inverse wave propagation problem