Course
CAAM 31230=STAT 31230
Title
Inverse Problems in Imaging
Instructor(s)
Guillaume Bal
Teaching Assistant(s)
TBA
Class Schedule
Sec 01: TR 11:00 AM-12:20 PM in Jones 226
Textbook(s)
TBA
Prerequisite(s)
 
Description

This course focuses on the mathematical description of many inverse problems that appear in geophysical and medical imaging: X-ray tomography, ultrasound tomography and seismic imaging, optical and electrical tomography, as well as more recent imaging modalities such as elastography and photo-acoustic tomography. Seen as reconstructions of constitutive parameters in differential equations from redundant boundary measurements, these continuous models tell us which parameters may or may not be reconstructed, and with which stability with respect to measurement errors. Time-permitting, we will also consider general methodologies to perform such reconstructions (regularization, optimization, Bayesian framework). Some knowledge of PDE and Fourier transforms is recommended.