Inverse problems of ultrasound tomography in models with attenuation

Abstract

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.

Continuous-wave ultrasonic tomography for oil/water two-phase flow imaging using regularized weighted least square framework

“…Besides the fan-beam angle transducer, another implementation in the measurement system is the design of high voltage bipolar square wave voltage excitation module. The amplitude of incident pressure is crucial for improving SNR of the received signal and the large attenuation caused by pipe's wall could be lethal to sufficient collection of the transmission signal (Goncharsky and Romanov, 2014). Here, a modified design of excitation module outputting a 100 Vp-p bipolar voltage square wave signal is presented with adjustable frequency, phase and duty cycle.…”

Supercomputer Simulations in Design of Ultrasound Tomography Devices

“…We use the iterative gradient method [4] to minimize the functional. Representations of the gradient Φ c (u(c, a)), Φ a (u(c, a)) were obtained in [3,5]. Finite difference time-domain method [6] was used to compute the wavefields.…”

“…The methods developed in the 1970s-1990s for solving inverse problems [8,9] are the most striking mathematical results of the last century. The inverse problem considered in this paper is a coefficient inverse problem [3]. The solution algorithms rely on the processing power of modern GPU clusters.…”

“…The images reconstructed from experimental data showed that a spatial resolution of ≈ 1.5 mm is attainable in a low-frequency setup with a central wavelength of ≈ 3 mm, which can be implemented in practice. The algorithms developed by the authors in [3,5] for layer-by-layer ultrasound tomography schemes were used to solve the inverse problems.…”

Supercomputer technologies in tomographic imaging applications

“…Breakthrough results in solving coefficient inverse problems are associated with the possibility to formulate explicitly and compute the gradient Φ (u(c)) of the residual functional. In various formulations, the expression for the gradient has been derived in the works [27,28,24,30]. According to [24], the gradient of the residual functional for the inverse problem (14-15) has the following form:…”