Ultrasound Image Reconstruction Using Nesterov's Accelerated Gradient

The purpose of this paper is to investigate Nesterov’s accelerated gradient (NAG) method for the reconstruction of speed of sound and attenuation images in ultrasound computed tomography. The inverse problem of reconstruction is tackled via minimizing the deviation between exact measurements and the predicted measurements based on a paraxial approximation of the Helmholtz equation which simulates the ultrasound wave forward propagation. To solve this optimization problem, NAG is performed and compared with other algorithms. Also, a line search method is used to compute the step size for each iteration since finding proper step sizes is crucial for the convergence of such optimization algorithms. The strong Wolfe conditions are adopted as the termination condition for line search. We have compared five algorithms, namely Gauss-Newton conjugate gradient, gradient descent, NAG, gradient descent with line search, and NAG with line search. On one hand, NAG with line search has the fastest convergence rate in respect to the number of used iterations compared to the other methods. However, due to the increased computational complexity of line search for each iteration, it requires extra computational time. On the other hand, NAG with a fixed step size for all iterations is the fastest method among all the tested methods regarding computational time.