MAGIC079: Inverse Problems

Course details

A core MAGIC course

Semester

Spring 2024
Monday, January 29th to Friday, March 22nd; Monday, April 22nd to Friday, May 3rd

Hours

Live lecture hours
9
Recorded lecture hours
1
Total advised study hours
40

Timetable

Thursdays
11:05 - 11:55 (UK)

Course forum

Visit the MAGIC079 forum

Description

This module provides a rigorous introduction to the mathematical theory of Inverse Problems. The lectures also include numerical experiments to develop first hand experience of the concepts covered by the theory.

The lectures are largely based on 3rd edition of the book An Introduction to the Mathematical Theory of Inverse Problems by Andreas Kirsch, Springer (2021). Most of the material is also covered in the previous editions of this book.

Prerequisites

This module assumes some knowledge of functional analysis and some minimal coding skills. Students can find a quick recap of functional analysis in Appendix A of the textbook.

Syllabus

(tentative syllabus)
  • Introduction to forward and inverse problems
  • General regularization strategies
  • Tikhonov regularization
  • Landweber iteration
  • Morozov's discrepancy principle
  • Regularization by discretization
  • Extension to nonlinear inverse problems
  • Optimization algorithms for PDE-constrained optimization

Lecturer

  • AP

    Dr Alberto Paganini

    University
    University of Leicester

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Assessment

The assessment for this course will be released on Monday 13th May 2024 at 01:00 and is due in before Friday 24th May 2024 at 12:00.

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.