Reconstruction of the ultrasound image using nesterov accelerated gradiant descent

In this thesis, ultrasound transmission tomography based on paraxial approximation has been investigated and acoustic wave propagation has been modeled to solve the forward problem. For iterative reconstruction, objective function was established between precise and predicted measurements obtained from the forward model. This objective function that is least square form, has been minimized by using various optimization methods. As optimization methods, gradient descent method and Gauss-Newton conjugate gradient has been compared in terms of computational time and convergence rate. The objective function convergence was achieved by combining the line search method with strong Wolfe condition and the gradient descent method. To improve this convergence rate, the BFGS (Broyden-Fletcher-Goldfarb-Shanno) method is combined with the gradient descent method. Line search method and BFGS method have been combined to further improve the efficiency of the improved convergence rate. Gradient descent, line search and BFGS optimization method as the fastest iterative algorithm was observed as the fastest iterative algorithm tested. In addition, benchmark optimization test functions were applied to optimization methods and compared. It has been concluded that the gradient descent, line search and BFGS method is a promising algorithm for image reconstruction in ultrasound tomography since the most modern Gauss - Newton conjugate method is analyzed with less iteration number