Ultrasound inverse scattering tomography for determination of speed of sound, density, and absorption using multiple freqyencies and views

Abstract

When the product of contrast and size of an object, which is to be reconstructed by using the ultrasound inverse scattering tomography algorithm, is large, it is well known that those algorithms fail to converge to a unique global minimum. In order to solve this well-known and difficult convergence problem, in this dissertation we present a new method, which converges to the true solution, for obtaining the scattering potential without using the Born or Rytov approximation. This method converts the nonlinear nature of the problem into a linear one. Through computer simulations we will show the validity of the new approach for high contrast two-dimensional scattering objects which are insonified by an incident ultrasound plane wave. Numerical results show that the reconstruction error is very small for circularly symmetric two-dimensional cylindrical objects whose refractive indices range from small to even sufficiently large values for which the previous inverse scattering algorithms fail to converge. Since the ultrasound cannot penetrate the gas or bones inside the human body, it is very difficult to obtain transmission data in many cases. In this case we must resort to the reflection mode imaging to get a quantitative parameter of interest. Another similar case arises when we want to image the human liver based on the ultrasound inverse scattering tomography. However, this is not the case when imaging the female breast since a full view scanning of it is possible. To overcome this difficulty, we propose a multiple frequency ultrasound inverse scattering tomography wherein multiple frequency sources are employed to obtain the scattered field data from the inaccessible view angles, thereby partially filling in the two-dimensional wavenumber spectrum of the object. We obtained good numerical results when the detectors are located on three or four sides of a square imaging grid, but our algorithm failed to produce a convergent solution when the detectors are loca...