Mathematics faculty and graduate students are invited to attend the PhD Defense of Scott Ziegler.

Date: Thursday, March 31, 2022
Time: 4:00 p.m.
Location: Weber 015

You may also attend by Zoom.

To Join visit: https://zoom.us/j/93212703154?pwd=cHAwb05QNHVGaWc0OTBOVG1SMG9yUT09
Meeting ID: 932 1270 3154
Passcode: 952733

Advisor:  Dr. Jennifer Mueller

Committee:  Dr. Margaret Cheney, Dr. Wolfgang Bangerth, Dr. Marlis Rezende

title: Full Waveform Inversion for Ultrasound Computed Tomography in the Deterministic and Bayesian Settings

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 extract 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 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 talk, we explore the use of 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 within a medium. 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.

You may also attend by Zoom.
To Join visit:  https://zoom.us/j/93212703154?pwd=cHAwb05QNHVGaWc0OTBOVG1SMG9yUT09
Meeting ID: 932 1270 3154
Passcode: 952733