Inverse problems of ultrasound tomography in models with attenuation

• Published in: Physics in medicine & biology Vol. 59; no. 8; pp. 1979 - 2004
• Main Authors: Goncharsky, Alexander V, Romanov, Sergey Y
• Format: Journal Article
• Language: English
• Published: England IOP Publishing 21.04.2014
• Subjects: Algorithms; breast cancer; Breast Neoplasms - diagnostic imaging; Image Processing, Computer-Assisted - methods; inverse coefficient problems; Models, Theoretical; supercomputer; ultrasonic tomography; Ultrasonography - methods; wave equations with attenuation
• ISSN: 0031-9155; 1361-6560
• DOI: 10.1088/0031-9155/59/8/1979

We develop efficient methods for solving inverse problems of ultrasound tomography in models with attenuation. We treat the inverse problem as a coefficient inverse problem for unknown coordinate-dependent functions that characterize both the speed cross section and the coefficients of the wave equation describing attenuation in the diagnosed region. We derive exact formulas for the gradient of the residual functional in models with attenuation, and develop efficient algorithms for minimizing the gradient of the residual by solving the conjugate problem. These algorithms are easy to parallelize when implemented on supercomputers, allowing the computation time to be reduced by a factor of several hundred compared to a PC. The numerical analysis of model problems shows that it is possible to reconstruct not only the speed cross section, but also the properties of the attenuating medium. We investigate the choice of the initial approximation for iterative algorithms used to solve inverse problems. The algorithms considered are primarily meant for the development of ultrasound tomographs for differential diagnosis of breast cancer.