LTCC Course: Computational Inverse Problems, fall 2015

Instructor: Dr. Bangti Jin (UCL)

Lecture time:  15:30 - 17:30

Lecture location: Cayley Room at De Morgan House

 

References:

1. Curtis Vogel. Computational Methods for Inverse Problems, SIAM, 2002.

2. Kazufumi Ito, Bangti Jin. Inverse Problems: Tikhonov Theory and Algorithms, World Scientific Press, 2014.

3. Jari Kaipio, Erkki Somersalo. Statistical and Computational Inverse Problems, Springer, 2005.

 

Course materials (slide & demo code)

lecture 1 (Oct. 5, 2015), matlab code test_tikhonov.m phillips.m get_l.m (The last two files are extracted from the popular tool Regutools due to Per Christian Hansen)

lecture 2 (Oct. 12, 2015), matlab code test_iterative.m

lectures 3 & 4 (Oct. 19, 26, 2015), matlab code test_ist.m  irls.m cdd.m test_greedy.m

lecture 5 (Nov. 2, 2015), matlab code MH_2d.m Gibbs_sampler.m

 

Assessment project: Please select one of the papers below. Then briefly sketch the approach, discuss the pros and cons of the approach in that paper for solving inverse problems, and validate your discussions with numerical experiments. For the numerics, begin with the simpler case of a random matrix, and then try the ill-conditioned problems, e.g. taking first derivatives, phillips (or other examples from Regutools). Please present your results in a pdf file (less than 10 pages, not including the code). The due date of the project report is November 20.

paper 1, paper 2, paper3