Autumn 2021 STAT 31230

Course: STAT 31230=CAAM 31230

Title: Inverse Problems in Imaging

Instructor(s): Guillaume Bal

Teaching Assistant(s): 

Class Schedule: Sec 1: TR 9:30 AM-10:50 AM in Jones 226

Textbook(s): TBA

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.