Open Access
Yun, Xingzhao
Graduate Program:
Computer Science and Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 22, 2019
Committee Members:
  • Almekkawy Mohamed, Thesis Advisor
  • ultrasound tomography
  • inverse scattering problem
  • regularization
Tumors are common in human body, but it will be lethal when cancer cells invade important organs. Therefore early detection is necessary for cancer treatment. Ultrasound Tomography(UT), as a non-invasive technology, has been widely used in decades. The goal of UT is to reconstruct the inner object based on it’s physical properties according to wave propagation in inhomogeneous environment. Multiple transmitters and multiple receivers make it possible to collect more data for image reconstruction, however, the regularization method for ill-posed problem and computational consuming are still two main challenges in UT. This thesis shows the results of the modeling and reconstruction of UT imaging for different simulated phantoms. One of the powerful approach that has been widely used in UT is the Distorted Born Iteration Method(DBIM), which is a method that iteratively solves forward problem and inverse problem for the inhomogeneities in the Region of Interest (ROI). Forward problem contains two sub-problems, computing total field and estimating the inhomogeneous Green’s function. Inverse problem solves scattering function of inner objects. Forward model is a well-posed system which makes it easy to solve. On the other hand, the principal computational challenge involved is the solution for ill-posed inverse problem, therefore the whole problem is considered to be an inverse scattering problem for simplicity. The first part of this work deals with theoretical aspects of ultrasound tomography and DBIM method. The inhomogensous wave propagation frame was derived as the mathematical background. Inverse model, forward model and Green’s function work for a valid reconstruction procedure have been shown in this thesis. The second part of this thesis dedicates to the computational cost in ill-conditioned inverse scattering problem. The comparison of several regularization methods including Truncated Total Least Squares (TTLS), Conjugate Gradient Least Squares (CGLS), Tikhonov and v-method are shown in this work. The contrast sensitive problem with different domains and their reconstruction performance with various noise conditions are addressed as well. Furthermore, the pros and cons of underdetermined system and overdetermined system for different regularization methods are demonstrated. Finally, the simulation results and conclusions on different aspects of conditions are discussed.