Full waveform inversion for ultrasound computed tomography in the deterministic and Bayesian settings
Date
2022
Authors
Ziegler, Scott, author
Mueller, Jennifer, advisor
Cheney, Margaret, committee member
Bangerth, Wolfgang, committee member
Rezende, Marlis, committee member
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Abstract
Ultrasound computed tomography (USCT) is a noninvasive imaging technique in which acoustic waves are sent through a region and measured after transmission and reflection in order to provide information concerning that region. There are many reconstruction techniques for USCT which rely on linearization of the total pressure field, but this simplifying assumption often causes a loss of resolution and poor results in highly reflective media. Full waveform inversion (FWI) is a method popularized by the geophysical community which makes use of entire time-dependent pressure measurements and repeated solutions of the nonlinear wave equation. Due to this lack of linearization, FWI is able to produce high-fidelity sound speed reconstructions, albeit at a steep computational cost. In this dissertation, we explore the use of the FWI techniques in both the deterministic and Bayesian settings. For the deterministic case, an algorithm for FWI is derived which makes use of the adjoint method for the computation of functional derivatives and the software package k-Wave for the solution of the nonlinear wave equation. This algorithm is tested on numerical breast and lung phantoms for a variety of regularization functionals and parameters, where it displays an excellent ability to reconstruct the size and shape of inhomogeneities. For the lung phantom, a novel application of a structural similarity index regularization term is used with an Electrical Impedance Tomography prior to speed convergence and improve organ boundary delineation. In the Bayesian setting, a Metropolis-adjusted Langevin FWI algorithm is proposed and tested on a simplified breast phantom, with an emphasis on reducing computational expense. Preliminary results from this test show promise for future research on FWI in the Bayesian framework.
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Subject
full waveform inversion
Markov chain Monte Carlo
Bayesian
ultrasound computed tomography
inverse problems