Three-Dimensional Ultrasound Tomography: Mathematical Methods and Experimental Results

This paper is concerned with developing the methods for solving inverse problems of ultrasound tomography under the model that accounts for diffraction, refraction and absorption. The inverse problem is posed as a nonlinear coefficient inverse problem for the wave equation. Iterative numerical algorithms have been developed to solve this inverse problem using supercomputers. The paper presents the results of 3D tomographic imaging of a test sample with acoustic properties close to those of human soft tissues. The data used for imaging were collected in a physical experiment on a test bench for ultrasound tomographic studies. The frequency range of sounding pulses was 50-800 kHz. The acoustic field was registered on a cylindrical surface surrounding the test sample. The 3D sound speed image was reconstructed using multistage iterative algorithm with gradually increasing signal bandwidth. The results showed that the tomographic methods developed can achieve a high spatial resolution while the contrast of the object doesn't exceed 20%. The proposed algorithms are designed for compact GPU clusters. Such clusters can be used as computing devices in medical tomographic facilities.