Math 5750 / 6880 Computational Inverse Problems
T Th 2:00 - 3:20 pm JTB 110
Instructor:
Prof. Elena Cherkaev
Office:
LCB 206
Phone:
581-7315
e-mail:
elena@math.utah.edu (put 5750/6880 in the subject line)
Office hours: T after class and by appointment
Class webpage: http://www.math.utah.edu/∼elena/M6880/math6880.html
Text: Computational Methods for Inverse Problems, Curtis Vogel, SIAM
Additional Texts: Rank Deficient and Discrete Ill-posed Problems, P.C. Hansen, 1998
Introduction to Inverse Problems in Imaging, M. Bertero and P. Boccacci, 1998
Parameter Estimation and Inverse Problems, R. Aster, B. Borchers, C. Thurber, 2005
Matlab codes can be downloaded from the authors’ website:
http://www.math.montana.edu/ vogel/
http://www2.imm.dtu.dk/ pch/Regutools/
Exams: There will be one take-home midterm. Tentative date for the midterm: Tuesday,
March 10. Final exam will be substituted by a final project.
Homework: Homework will be assigned and a large portion of the problems will be
graded. You are encouraged to discuss homework problems with friends and make study
groups, but each homework should be written individually. The homework problems
will be theoretical and computational. You can use any software of your choice for
computational assignments.
Grading: The homework will count for 40% of the grade, midterm and project will
count for 30% each.
Course Outline Math 5750/6880 studies ill-posed inverse and imaging problems, among
them are parameter estimation problems, signal processing, inverse problems for integral
equations, statistical inverse problems, ill-posed optimization problems. Applications
are numerous, we will discuss formulation and examples of inverse problems in medical
and geophysical imaging, non-destructive testing and image processing, optical imaging
and inverse bioelectric problem, inverse scattering and electric sounding, acoustic and
seismic imaging, ultrasound and X-ray computed tomography, optimal design and electromagnetic imaging. The studied techniques are de-convolution methods, ill-posedness,
various regularization techniques, choice of regularization parameters, iterative methods
for non-linear problems, statistical estimation methods, variational methods and nonconvex optimization techniques in image processing.
The course is addressed to graduate and senior undergraduate students in mathematics,
science, and engineering.
ADA statement: The American with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning,
and psychiatric disabilities. Please contact me at the beginning of the semester to discuss
any such accommodations for the course.