COMP0114 Inverse Problems in Imaging

This database contains the 2018-19 versions of syllabuses. These are still being finalised and changes may occur before the start of the session.

Syllabuses from the 2017-18 session are available here.

Academic session

2018-19

Module

Inverse Problems in Imaging

Code

COMP0114

Module delivery

1819/A7P/T2/COMP0114 Postgraduate

Related deliveries

1819/A7U/T2/COMP0114 Masters (MEng)

Prior deliveries

COMPGV08

Level

Postgraduate

FHEQ Level

L7

FHEQ credits

15

Term/s

Term 2

Module leader

Arridge, Simon

Contributors

Arridge, Simon

Module administrator

Nessa, Yasmin

Aims

To introduce the concepts of optimisation, and appropriate mathematical and numerical tools applications in image processing and image reconstruction.

Learning outcomes

On successful completion of the module, a student will be able to:

  1. To understand the principles of optimisation and to acquire skills in mathematical methods and programming techniques.

Availability and prerequisites

This module delivery is available for selection on the below-listed programmes. The relevant programme structure will specify whether the module is core, optional, or elective.

In order to be eligible to select this module as optional or elective, where available, students must meet all prerequisite conditions to the satisfaction of the module leader. Places for students taking the module as optional or elective are limited and will be allocated according to the department’s module selection policy.

Programmes on which available:

  • MRes Computational Statistics and Machine Learning
  • MRes Robotics
  • MRes Virtual Reality
  • MSc Computational Statistics and Machine Learning
  • MSc Computer Graphics, Vision and Imaging
  • MSc Machine Learning
  • MSc Robotics and Computation
  • MRes Medical Physics and Biomedical Engineering
  • MSc Scientific Computing

Prerequisites:

Students should have taken the term 1 module Machine Vision (COMP0137). Please contact the instructor if you have not taken this module and still want to enroll.

In order to be eligible to select this module, students must have a strong competency in mathematical and programming skills, including:

  • Fourier Theory (discrete and continuous; sampling; convolution);
  • Linear Algebra (Eigenvalues and Eigenvectors; Matrix Algebra)
  • Calculus (functions of multiple variables; calculus of variation)
  • Probability (Gaussian and Poisson probabilities; Bayes Theorem)
  • Matlab programming (multidimensional arrays; image visualisation; anonymous functions)

Students should take the self-test available here http://www0.cs.ucl.ac.uk/staff/S.Arridge/teaching/optimisation/GV08test.pdf to assess their mathematical ability for this course

Content

  • Introduction
    • Example problems
    • Data Fitting Concepts
    • Existence
    • Uniqueness
    • Stability
    • Bayesian interpretation
  • Mathematical Tools
    • Linear Algebra
      • Solving Systems of Linear Equations
      • Over and Under Determined Problems
      • Eigen-Analysis and SVD.
    • Variational Methods
      • Calculus of Variation
      • Multivariate Derivatives
      • Frechet and Gateaux Derivatives
    • Regulariation
      • Tikhonov and Generalised Tikhonov
      • Non-Quadratic Regularisation
      • Non-Convex Regularisation
      • Methods for selection of regularisation parameters
  • Numerical Tools
    • Descent Methods
      • Steepest Descent
      • Conjugate Gradients
      • Line Search
    • Newton Methods
      • Gauss Newton and Full Newton
      • Trust-Region and Globalisation
      • Quasi-Newton
      • Inexact Newton
  • Optimisation Methods
    • Least-Squares Problems
      • Linear Least Squares
      • Non-linear Least Squares
    • Non-Quadratic Problems
      • Poisson Likelihood
      • Kullback-Leibler Divergence
    • Lagrangian penalties and constrained optimisation
    • Proximal methods
  • Concepts of sparsity
    • L1 and total variation
    • wavelet compression
    • dictionary methods.
  • Bayesian Approach
    • Maximum Likelihood and Maximum A Posteriori estimates
    • Expectation-Minimisation
    • Posterior Sampling
      • Confidence-Limits
      • Monte Carlo Markov Chain
  • Applications
    • Image Denoising
    • Image Deblurring
    • Inpainting
    • Linear Image Reconstruction
      • Tomographic Reconstruction
      • Reconstruction from Incomplete Data
    • Non-Linear Parameter Estimation
    • General Concepts
    • Direct and Adjoint Differentiation
  • Other Approaches
    • Learning Based Methods

An indicative reading list is available via http://readinglists.ucl.ac.uk/departments/comps_eng.html.

Delivery

The module is delivered through a combination of lectures, tutorials, seminars, written and programming exercises, and project work.

Assessment

This module delivery is assessed as below:

#

Title

Weight (%)

Notes

1

Coursework 2

20

 

2

Coursework 1

20

 

3

Literature critique

10

 

4

Project report

50

 

In order to pass this module delivery, students must achieve an overall weighted module mark of 50%.