Multistage Iterative Method to Tackle Inverse Problems of Wave Tomography - Goncharsky, Alexander V.; Romanov, Sergey Y.; Seryozhnikov, Sergey Y. (Supercomputing Frontiers and Innovations, 2022)
This paper is concerned with developing the methods for solving inverse problems of lowfrequency ultrasound tomography under scalar wave models using supercomputer technologies. Unlike X-ray tomography, the inverse problem considered is posed as a problem of minimizing a non-convex residual functional. The multistage iterative method (MSM) is proposed as a method for obtaining an approximate solution to the inverse problem. Convergence of the method to the exact solution is achieved via the use of low-frequency sounding signals at the initial stages of the iterative method. The method is illustrated on model problems focused on ultrasound tomographic diagnostics of soft tissues in medicine. Finite-difference time-domain method is used to solve the wave equation, which accounts for most of the computational complexity of the method. The multistage method reduces the computation time, since the initial stages use low-resolution finite difference grids. The effectiveness of the MSM method is investigated on GPU and SIMD-capable CPU computing platforms. Numerical simulations showed that modern processors equipped with AVX-512 FPUs are capable of solving small-scale problems of wave tomography. For large-scale tasks, GPUs equipped with fast on-board memory are preferred. The numerical algorithm is data-parallel and well-suited for GPU architecture. The proposed method can be used in medical imaging and nondestructive testing applications.