ELEC 404
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ELEC 404: Imaging and Inference
This paper will be taught in the second semester and consist of two lectures per week.
Timetable
Tuesday, Friday 11am, Rm 312
Content:
The linear inverse problem, singular value decomposition, regularization methods, an example in image deblurring, statistical description of inverse problems, Bayesian statistical inference, estimators and the Cramer-Rao lower bound, recursive estimators and Kalman filters, stochastic simulation, Markov chains, sampling from posterior probability densities using the Metropolis-Hastings algorithm, output analysis.
Prerequisites
There are no specific prerequisites, however PHSI 461 is strongly recommended preparation. Papers in analysis of experiments, probability, inference, and programming will also be useful preparation for ELEC 404.
Study Guide:
Information on coursework, recommended reading, etc, in pdf.
Course Material in Electronic Form
Course notes written by Sze M Tan, Colin Fox and Geoff K. Nicholls. You will need the Adobe Acrobat Reader to view or print.
Course Notes:
- Chapter 1: (updated 17 July 2009) Introduction to Inverse Problems
- Chapter 2: (updated 4 August 2009) Linear Transformations
- Chapter 3: (updated 4 August 2009) Regularization Methods for Linear Inverse Problems
- Chapter 4: (updated 18 August 2009) Introduction to Probability and Statistics
- Chapter 5: (updated 25 August 2009) Bayesian Statistical Inference and Parameter Estimation
- Chapter 6: The Recursive Linear Inverse Problem
- Chapter 7: Stochastic Simulation
- Chapter 8: Sampled Solutions to Inverse Problems
- Chapter 9: Output Analysis
Additional Reading:
on regularization:
- Rank-Deficient and Discrete Ill-Posed Problems by Per Christian Hansen is published by SIAM
- Computational Methods for Inverse Problems by Curt Vogel, also published by SIAM
on probability:
- A free text on probability is the online AMS text Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. Individual chapters available here, answers to odd exercises and further information available here.
- I strongly recommend the book Probability and Random Processes by Geoffrey Grimmett and David Stirzaker (google book link). If you are likely use random processes in the future, I suggest you buy a copy.
on sample-based inference (MCMC):
- Lecture notes (by Geoff Nicholls) from a workshop on Bayesian Methods in Inverse Problems in Kuopio, Finland, July 2004 on Bayesian Inference and Markov Chain Monte Carlo by Example
- A video lecture on Markov Chain Monte Carlo Methods by Christian Robert
SmartBoard Lectures in 2009
| Introduction and deblurring example | 1 (14 July) | 2 (17 July) | 3 (21 July) |
| Linear inverse problems | 4 (24 July) | 5 (28 July) | 6 (31 July) |
| Regularization | 7 (4 Aug.) | 8 (7 Aug.) | 9 (11 Aug.) |
| Probability | 10 (15 Aug.) | 11 (18 Aug.) | 12 (21 Aug.) |
| Bayesian inference | 13 (25 Aug.) | 14 (28 August) | 15 (8 September) |
| Stochastic simulation | 16 (11 September) | 17 (15 September) | 18 (18 September) |
| Reversible Markov chains | 19 (22 September) | 20 (25 September) | 21&22 (29 Sept & 6 Oct) |
| Sample-based image analysis | 23 (9 October) | 24 (13 October) |
Assignments in 2009
- Assignment 1: download and associated files blurry.tif (right click to 'Save Link As'), blurpic.m (right click to 'Save Link As')
- Assignment 2: download
- Assignment 3: download
Stuff from previous years
ELEC 404 is a continuation of paper Physics 707 Inverse Problems that was taught at Auckland University from 1995 to 2006. You will find exam papers, course material, examples, and assignments from previous years (of Physics 707 Inverse Problems) in ELEC 404 Past Material
Please address comments and queries to Colin Fox.
Links
Timetables and Paper Details
