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ELEC 404: Imaging and Inference (2011 semester 2)

This paper is being taught by Colin Fox. There are (usually) three lectures per week.

Timetable

Tuesday (11am, Rm 311), Wednesday (11am, Rm 311), Thursday (2pm, Rm 311)

Content:

The linear inverse problem, singular value decomposition, regularization methods, an example in image deblurring, problems with least-squares and regularization, the role of probability in 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

We are still using the 2009 version of the course notes written by Sze M Tan, Colin Fox and Geoff K. Nicholls. Colin intends (!) to update these notes: updates will be announced as they become available.

Course Notes:

• Chapter 1: Introduction to Inverse Problems
• Chapter 2: Linear Transformations
• Chapter 3: Regularization Methods for Linear Inverse Problems
• Chapter 4: Introduction to Probability and Statistics
• Chapter 5: 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

You can download the complete course notes as a book here: ELEC404 Inverse Problems notes

Additional Material:

on regularization:

• Rank-Deficient and Discrete Ill-Posed Problems by Per Christian Hansen is published by SIAM. Check out the nice MatLab package.

• 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. Answers to odd exercises and further information available here.
• I heartily 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

Assignments in 2011

• Assignment 1 and associated files polydata.txt (right click to 'Save Link As'), jupiter1.tif (right click to 'Save Link As'), jupiter.m (right click to 'Save Link As')

Stuff from previous years

ELEC 404 in 2009

Please address comments and queries to Colin Fox.

Links

The University's 'official' site where you can find out the cost of taking ELEC 404, and other Paper Details