Course details
Semester
- Spring 2022
- Monday, January 31st to Friday, March 25th; Monday, April 25th to Friday, May 6th
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Tuesdays
- 12:05 - 12:55 (UK)
Description
If any of these elements are unknown or unavailable, then the field problem becomes improperly defined (ill-posed) and is of an indirect (or inverse) type.
The course will give an introduction to Inverse Problems.
Various mathematical and numerical techniques for solving inverse problems will be described.
Prerequisites
Also just enough physics to understand the phenomena of heat conduction, fluid flow, acoustics, optics and electromagnetism used to formulate the forward problems.
Syllabus
- Basic linear inverse problems - enough linear algebra and functional analysis to understand ill-conditioning and regularization of inverse problems.
- Basic techniques for linear inverse problems - truncated singular value decomposition, Tikhonov's regularization, parameter choice methods, etc.
- PDE theory for inverse problems - enough to read the main existence, uniqueness and stability papers, e.g. Isakov's book. Some mathematical techniques and concepts, e.g. Schauder fixed point theorem, contraction principle, Fredholm alternative, etc.
- Numerical methods for inverse problems including FEM and BEM for forward problem solution and iterative regularization methods. Level set method. Constrained minimization gradient based methods.
Lecturers
-
DL
Professor Daniel Lesnic
- University
- University of Leeds
- Role
- Main contact
-
SH
Dr Sean Holman
- University
- University of Manchester
Bibliography
No bibliography has been specified for this course.
Assessment
The assessment for this course will be released on Monday 9th May 2022 at 00:00 and is due in before Monday 23rd May 2022 at 11:00.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
Only current consortium members and subscribers have access to these files.
Please log in to view course materials.
Lectures
Please log in to view lecture recordings.