Supercomputer Simulation Study of the Convergence of Iterative Methods for Solving Inverse Problems of 3D Acoustic Tomography with the Data on a Cylindrical Surface
This paper is dedicated to developing effective methods of 3D acoustic tomography. The inverse problem of acoustic tomography is formulated as a coefficient inverse problem for a hyperbolic equation where the speed of sound and the absorption factor in three-dimensional space are unknown. Substantial difficulties in solving this inverse problem are due to its nonlinear nature. A method which uses short sounding pulses of two different central frequencies is proposed. The method employs an iterative parallel gradient-based minimization algorithm at the higher frequency with the initial approximation of unknown coefficients obtained by solving the inverse problem at the lower frequency. The efficiency of the proposed method is illustrated via a model problem. In the model problem an easy to implement 3D tomographic scheme is used with the data specified at a cylindrical surface. The developed algorithms can be efficiently parallelized using GPU clusters. Computer simulations show that a GPU cluster capable of performing 3D image reconstruction within reasonable time.
KeywordsUltrasound tomography Medical imaging Inverse problem Gradient method
This work was supported by Russian Science Foundation [grant number 17-11-01065]. The research is carried out at Lomonosov Moscow State University. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.
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