Course unit details:
Mathematical Foundations Of Imaging
| Unit code | IIDS67451 |
|---|---|
| Credit rating | 15 |
| Unit level | FHEQ level 7 – master's degree or fourth year of an integrated master's degree |
| Teaching period(s) | Semester 1 |
| Offered by | Division of Informatics, Imaging and Data Sciences |
| Available as a free choice unit? | No |
Overview
The course unit will use lectures, ‘pencil and paper’ exercises and some basic programming to introduce students to a number of fundamental mathematical and scientific concepts that underpin the majority of the imaging course units that form the remainder of the programme. These are:
Statistics and Probability
Summary statistics, hypothesis testing, multivariate statistics, normal, binomial, Poisson, Chi-square distributions. Discrete and continuous probability, probability density, conditional probability, Bayes theorem.
Linear Algebra and Geometry
Linear algebra, transition matrices, geometric transforms, eigenvalue methods, tensors, model fitting (least squares), representing lines, planes and regions.
Fourier Methods
Fourier Series, Fourier Transform, convolution, Linear Time/Space Invariant Systems point spread function, modulation transfer function, image reconstruction.
Introduction to programming: Basic numerical programming in MATLAB and Python (NumPy/SciPy).
Aims
Provide students with the mathematical and scientific foundation necessary to undertake the imaging course units.
The material in this course unit provides a common knowledge and skill base for the remainder of the programme. Students from a physical science background may have some experience in some of this material. However, few will have developed the full skill set required in these specific topics. Most of the material will be new to students from a non-physical science background, but the introductory maths and physics in the Basic Skills course unit should provide them with a basis to advance to this content.
Learning outcomes
|
Category of outcome |
Students will be able to: |
|
Knowledge and understanding |
Understand the underlying principles and applications of statistics and probability relevant to imaging. Understand the application of matrices in linear algebra and have a basic insight into eigenvalue problems. Understand the basic ideas and applications of Fourier methods applied to imaging. |
|
Intellectual skills |
Be able to apply mathematical and statistical knowledge to the understanding of imaging techniques and more widely in scientific investigations. |
|
Practical skills |
Solve moderately complex mathematical and numerical problems. Apply mathematical and statistical techniques to analysing scientific data. Use programming language (Python or MATLAB) for numerical problem solving and run basic program scripts. |
|
Transferable skills and personal qualities |
Have increased confidence in dealing with statistical and mathematical concepts. |
Teaching and learning methods
The course unit will consist of 12 sessions, most of which will consist of a lecture together with written individual and group exercises. On-line formative quizzes will be used as appropriate. Some concepts will be reinforced using MATLAB exercises, and basic techniques for setting up and solving linear equations using Python will be introduced.
Sessions 1-4: Solving problems in linear algebra. Introductions to geometry and basic Python.
Sessions 5-8: Statistical summaries of data, probability and measurement error, statistical validity.
Sessions 9-12: Representation of images, Fourier methods, Image reconstruction, and Inverse problems.
There will also be five sessions introducing programming, in which students will be able to carry out exercises in the topics delivered in lecture sessions. There will be no summative assessment associated with these sessions.
Assessment methods
| Method | Weight |
|---|---|
| Written exam | 50% |
| Practical skills assessment | 20% |
| Set exercise | 30% |
Formative: Problem sheets after each lecture
Set Exercise: MCQ Statistics = 30%
Basic programming assignments = 2 x 10%
Feedback methods
- Formal summative assessments
- Real time educative formative assessments during practical classes
Study hours
| Scheduled activity hours | |
|---|---|
| Lectures | 36 |
| Independent study hours | |
|---|---|
| Independent study | 114 |
Teaching staff
| Staff member | Role |
|---|---|
| Timothy Cootes | Unit coordinator |