USCT Image Reconstruction: Acceleration using Gauss-Newton Preconditioned Conjugate Gradient

In this paper, we solve the inverse problem of image reconstruction in ultrasound transmission tomography, proposing a two-level strategy with an outer and an inner loop. At each iteration of the outer loop, the system is linearized and this linear subproblem is solved in the inner loop with a preconditioned conjugate gradient. A standard Cholesky preconditioning method based on the system matrix is compared with a matrix-free Quasi-Newton update approach, where a preconditioned matrix-vector product is computed at the beginning of every CG iteration. We also use a multigrid scheme with multi-frequency reconstruction to get a convergent rough reconstruction at a lower frequency and then refine it on a higher-resolution grid.