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Course Schedule

Week Lecture Date Lecture Notes Homeworks
1 1 Dec 7, 2011 Introduction to inverse and ill-posed problems Read Chapter 1 of Parker (1994)
1 2 Dec 9, 2011 Mathematical background: linear algebra, Note -
2 3 Dec 13, 2011 Mathematical background: functional analysis Assignment 1 (due date Dec 20,2011)
2 4 Dec 15, 2011 Linear inverse problems and regularization of ill-posed problems Read Chapters 1 and 2 of Vogel (2002)
3 5 Dec 19, 2011 Review session -
3 6 Dec 22, 2011 Regularization and Optimization Theory Assignment 2 (due date Dec 29,2011)
4 7 Dec 26, 2011 Numerical optimization Read Chapters 3 of Vogel (2002)
4 8 Dec 29, 2011 Iterative Methods -
5 9,10 Jan 5, 2011 Convex optimization using iterative methods: steepest descent, conjugate gradient, and Newton's methods -
6 11 Jan 9, 2011 Nonlinear optimization using steepest descent and conjugate gradient methods, Rosenbrock function, inexact line search, Wolfe's conditions Assignment 3, data file (due date Jan 23,2012)
6 12-13 Jan 12 2011 Preconditioned conjugate gradient, nonlinear conjugate gradient, quasi-Newton method, 1D image deblurring -
7 14 Jan 23, 2011 Non-uniqueness in linear inverse problems (revisited), Statistical estimation theory -
8 15-16 Jan 26, 2011 Methods for choosing regularization parameter (Discrepancy principle, L curve, unbiased predictive risk estimator), Parameter identification and adjoint method -
9 17 Jan 30, 2012 Project proposal presentation (5 minutes per person), an application of adjoint method to seismic inversion, linearization of nonlinear inversion -
9 18 Feb 2, 2012 Review session: Non-uniqueness and resolution analysis of linear inverse problem, adjoint method in seismic imaging -
10 19 Feb 6, 2012 Occam's inversion, smoothness constraint, calculation of Frechet's derivative Project proposal due, Assignment 4 (due date Feb 27,2012)
10 20 Feb 9, 2012 Lab: Linearized inversion to solve the Rosenbrock function -
11 21 Feb 13, 2012 Lab: 1D Line search for optimal step length using the Wolfe's conditions. Use Rosenbrock function as an example -
11 22 Feb 16, 2012 Lab: Solving the Rosenbrock function using stochastic methods: genetic algorithm, particle swarm, simulated annealing -
12 23 Feb 20, 2012 Lab: Solving the Rosenbrock function using stochastic methods: genetic algorithm, particle swarm, simulated annealing (continued) -
13 24 Feb 27, 2012 Joint inversion by Puwis
Readings: Paper 1, Paper 2
Assignment 5 (due date Feb 28,2012)
13 25 Mar 1, 2012 Lab: smoothness constraint and total variation (Vogel, 2002; Chapter 8) -
14 26 Mar 5, 2012 Lab: Total variation (Vogel, 2002; Chapter 8) Assignment 6 (due date March 9,2012)
14 27 Mar 8, 2012 Bayesian inversion (Aster et al., 2005; Chapter 11) -
15 28 Mar 12, 2012 Model and data resolution matrices (Aster et al., 2005; Section 4.2) -
15 29 Mar 15, 2012 Term project discussion -
16 30 Mar 29, 2012 Term Project Presentation Project report due on April 5