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 |