Personal tools
You are here: Home → Education → Graduate Study at FMRIB → Program → Course Syllabus → Adv Maths and Analysis Syllabus
 
Document Actions

Adv Maths and Analysis Syllabus

A following gives a description of the Advanced Maths and Analysis Course for 2011/12 (current program is preliminary and subject to revision)

Aim

On completing the course, attendees will:
  • Have a more detailed understanding of several mathematical areas of fundamental importance in image analysis.
  • Have a mathematical understanding of how key FSL tools work and be able to appreciate the strengths and limitations of their algorithms.
  • Be able to easily extend their knowledge in the different topics by further readings of book chapters and relevant journal publications.

Syllabus

The course is divided into five sessions, each covering a separate topic:


Signal and image processing

  • Fourier analysis of signals and images
  • Wavelets and time/frequency analysis
Suggested pre-readings:
Further Readings:
     Bracewell, The Fourier Transform and its Applications
     Mallat, A Wavelet Tour of Signal Processing
     Gonzalez and Woods, Digital Image Processing


Bayesian Modelling

  • Conditional Probabilities and Marginalisation
  • Likelihood and Posterior
  • Bayesian inference (incl. Laplace Approximation and MCMC)
  • Bayesian Model Selection
Suggested pre-readings:
     Andrew Gelman, Bayesian data analysis (chapters 1&2 available on Google Books)
Further Readings:
     Andrew Gelman, Bayesian Data Analysis
     Bradley P. Carlin, Thomas A. Louis, Bayes and Empirical Bayes Methods for Data Analysis
     C Bishop, Pattern Recognition and Machine Learning


Machine Learning for Regression

  • Linear and nonlinear regression
  • Kernel methods
  • Gaussian processes
Suggested pre-readings:
     C Bishop, Pattern Recognition and Machine Learning


Machine Learning for Classification

  • K-means / C-means
  • Gaussian mixture models
  • Linear discriminant analysis
  • Support-vector machines
Suggested pre-readings:


Further Statistics

  • Randomise in-depth
  • Repeated Measures - general methods
  • Repeated Measures - special cases
  • Sandwich Estimators
Suggested pre-readings:

Assessment

This course is not assessed.

Course Organisation

This course is organised by Dr Saad Jbabdi and Dr Mark Jenkinson.
Email: {saad,mark}@fmrib.ox.ac.uk