Abstract
In this paper, we propose a matrix-free 3D ultrasonic reconstruction scheme based on the Fast Iterative Shrinkage-Thresholding algorithm (FISTA) implemented on a GPU. The matrix-free implementation allows to reconstruct images even for problem sizes that would be intractable when explicitly calculating the matrix. However, due to the matrix-free implementation, additional steps are necessary to estimate the stepsize parameter required by FISTA, since the optimal stepsize depends on the largest singular value of the operator matrix, which in the matrix-free version is unavailable and cannot be built due to its size. The estimation is performed based on a priori knowledge of the model. We compare our method to 3D SAFT and OMP images of volumetric ultrasound measurement data of a steel specimen to show how FISTA leads to sharper images facilitating sizing and locating of defects within a specimen.