Inverse Theory and Applications


Instructor: Chaiwoot Boonyasiriwat (chaiwoot@gmail.com)
Class Hours: Friday (1:00PM-4:00PM)
Class Room: P503
Assessment: homework 70%, project 30%
Syllabus: PDF
Codes: - Regularization Tools (original site, MATLAB Central, regtools.zip)

Tentative Schedule

Week Date Topics Assignments
1 Aug 16, 2019 Introduction to inverse problems, examples of inverse problems, classification of problems, linear regression, linear least squares, weighted least squares, L1 regression
Lab 1: linear regression
Assignment 1
2 Aug 23, 2019 Functional spaces (Euclidean space, metric space, inner product space, Hilbert space)
Lab 2: 1D image deblurring
Assignment 2
3 Sep 6, 2019 Rank deficiency, generalized inverse, instability, Tikhonov regularization
Lab 3: 2D straight-ray traveltime tomography (ray.m, stt_mod.m, stt_mod2.m)
4 Sep 13, 2019 local optimization algorithms
Lab 4: Finding the minimum of the Rosenblock's function using local optimization methods
Assignment 3, hw3.zip
5 Sep 20, 2019 Quasi-Newton methods
Lab 5: Finding the minimum of the Rosenblock's function using local optimization methods
6 Sep 27, 2019 Metaheuristic optimization methods
Lab 6: Finding the minimum of the Rosenblock's and Ackley's functions using metaheuristics methods. Solving the traveling saleman problem using simulated annealing.
7 Oct 9, 2019 Nonlinear inverse problem, fast sweeping method
Lab 7: Implementation of the fast sweeping method and ray tracing (fsm.m, vel_nx1841_nz601_dx5.dat)
8 Oct 25, 2019 adjoint-state method, functional derivative, traveltime tomography based on the adjoint method,
Lab 8: curved-ray traveltime tomography based on the Jacobian, ctt2.zip
9 Nov 1, 2019 adjoint method, inverse scattering
Lab 9: Traveltime tomography: gradient computation using the adjoint method, time-domain waveform modeling and inversion
10 Nov 8, 2019 Inverse scattering (continued), frequency-domain waveform modeling
Lab 10: time-domain inverse scattering
11 Nov 15, 2019 Deep learning for inverse problems
12 Nov 22, 2019 Deep learning for inverse problems (continued) keras.zip
13 Nov 29, 2019 TBA
15 Nov 29, 2019 Project presentation

References

Inverse Problems

Optimization