MA32057: Inverse problems and numerical optimisation
[Page last updated: 22 May 2025]
| Academic Year: | 2025/26 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 10 [equivalent to 20 CATS credits] |
| Notional Study Hours: | 200 |
| Level: | Honours (FHEQ level 6) |
| Period: |
- Semester 2
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| Assessment Summary: | CWRI 25%, EXCB 75% |
| Assessment Detail: |
- Closed-book written examination (EXCB 75%)
- Coursework (CWRI 25%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must take MA32065
In taking this module you cannot take MA40050
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| Learning Outcomes: |
By the end of the course, students should understand the concepts of ill-posedness and regularisation, be able to analyse variational regularisation problems, have a basic understading of convexity and its role in numerical optimisation, and be able to use a range of modern iterative optimisation methods for solving inverse problems.
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| Synopsis: | Inverse problems arise from the need to obtain information about an object of interest from indirect measurements. Typical applications include medical imaging, non-destructive testing, and geosciences. A common feature of such problems is their sensitivity to errors in the observed data, which renders naive inversion methods unstable. In this course we will study regularisation techniques that can stabilise the inversion and numerical optimisation algorithms that such techniques require.
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| Content: | Inverse problems, ill-posedness. Regularisation (e.g., iterative regularisation, variational
regularisation). Basic concepts of convex analysis. Convex non-smooth optimisation methods.
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| Course availability: |
MA32057 is Optional on the following courses:
Department of Computer Science
- USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
Department of Economics
- UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 3)
- UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
- UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
- UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB30 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 3)
- USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 4)
- USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 4)
Department of Physics
- USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 3)
- USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
- USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
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Notes: - This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
- 好色tv and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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