Ultrasound Image Reconstruction Using Nesterov's Accelerated Gradient (original) (raw)

The aim of this thesis is to conduct research on Nesterov’s accelerated gradient method for the reconstruction of speed of sound as well as attenuation profiles in ultrasound computed tomography. Firstly, ultrasound (acoustic) wave propagation based on paraxial approximation has been performed as the forward model. For iterative reconstruction, exact measurements have been simulated from the forward model and then compared with the estimated measurements which are updated for each iteration based on the reconstructed profiles. This process is known as an inverse problem, which is tackled via minimizing the deviation between exact measurements and estimated measurements, i.e. via solving a nonlinear least-squares problem. To minimize this deviation, Nesterov’s accelerated gradient method has been performed and compared with other optimization algorithms including gradient descent and Gauss-Newton conjugate gradient. Also, two line search (LS) methods have been used to choose the step size for each iteration since finding proper step size is crucial for the convergence of such optimization algorithms. One line search method is backtracking and the other is based on zoom functions. The Wolfe conditions and strong Wolfe conditions have been adopted as the termination condition for line search. In total, seven methods of different combinations of the above algorithms have been tested. These methods are Gauss-Newton conjugate gradient, gradient descent with fixed step size, Nesterov’s accelerated gradient with fixed step size, gradient descent with backtracking LS step size under Wolfe conditions, Nesterov’s accelerated gradient with backtracking LS step size under Wolfe conditions, gradient descent with zoom LS step size under strong Wolfe conditions, Nesterov’s accelerated gradient with zoom LS step size under strong Wolfe conditions. Among the seven methods, Nesterov’s accelerated gradient with LS step size has the fastest convergence rate (iteration number) compared to other methods. However, due to the increased computational complexity of LS for each iteration, it requires extra computational time. On the other side, Nesterov’s accelerated gradient with a fixed step size is the fastest method among all the tested methods regarding computational time. We conclude that Nesterov’s accelerated gradient is a promising algorithm for the image reconstruction in ultrasound transmission tomography, due to its relatively cheap computation per iteration as compared with the state-of-the-art Gauss-Newton conjugate gradient method.