Course Catalog 2007-2008

MAT-52506 INVERSE PROBLEMS, 6 cr
Inverse Problems

Courses persons responsible
Samuli Siltanen

Language of Instruction
If one or more students do not speak Finnish, then all teaching is given in English.

Implementations
Person responsible: Samuli Siltanen
  Period 1 Period 2 Period 3 Period 4 Period 5 Summer
Lecture 4 h/week 4 h/week - - - -
Exercise 2 h/week 1 h/week - - - -
Exercise work - 2 h/week - - - -
Exam  
(Timetable for academic year 2007-2008)

Objectives
Examples of inverse problems include medical imaging (CT, MRI), underground prospecting for ores using electrical measurements, recovering the shape of an asteroid from lightcurve observations, and sharpening a blurred photograph. These problems are sensitive to measurement errors: straightforward inversion attempts lead to failure. Therefore spezialized solution methods are needed. This course gives an overview of classical and modern solution methods for inverse problems. Both theory and computer implementation are discussed, and the methods are demonstrated with practical inverse problems involving measured data.

Content
Content Core content Complementary knowledge Specialist knowledge
1. Inversion of Radon transform of 3D X-ray tomography.       
2. Singular value decomposition of a matrix and solution by SVD truncation. Classical and generalized Tikhonov regularization.       
3. Total variation regularization with emphasis on implementation issues.       
4. Introduction to statistical (Bayesian) inversion. Theory and implementation of Monte Carlo Markov Chain methods.       
5. Practical applications to medical imaging and signal processing.       

Requirements for completing the course
Passed exam, sufficient activity in exercises, accepted Matlab project work.

Evaluation criteria for the course

  • Used assessment scale is numeric (1-5)

    • Study material
    Type Name Auhor ISBN URL Edition, availability... Exam material Language
    Lecture slides Inverse Problems Fox, Nicholls, Tan   http://www.math.auckland.ac.nz/%7Ephy707/   No  English 
    Online book Inversio-ongelmat Erkki Somersalo   http://www.math.hut.fi/teaching/invvanha/indexvanha.html.fi   No  Finnish 
    Lecture slides Käänteiset ongelmat Jari Kaipio   http://venda.uku.fi/studies/virtual/KON/KON1/lectures/main.pdf   No  Finnish 
    Lecture slides Inverse Problems Samuli Siltanen   http://matriisi.ee.tut.fi/courses/MAT-52500/course.html   Yes  English 

    Prerequisites
    Prequisite relations (Sign up to TUT Intranet required)

    Remarks

  • Partial passing of course must be in connection with the same round of implementation.

  • The course is suitable for postgraduate studies.

    • Distance learning

  • ITC utilized during the course

    • - In information distribution via homepage, newsgroups or mailing lists, e.g. current issues, timetables
    - In compiling teaching material, particularly for online use or other electronic media
    - In compiling exercise, group or laboratory work
    - In distributing and/or returning exercise work, material etc
    - In the visualization of objects and phenomena, e.g. animations, demonstrations, simulations, video clips

  • Estimate as a percentage of the implementation of the course

    • - Contact teaching: 80 %
    - Distance learning: 0 %
    - Proportion of a student's independent study: 20 %

    Correspondence of content
    MAT-52500 Inverse Problems

    Course homepage

    Last modified 09.02.2007
    Modified bySamuli Siltanen