MAT-62006 Inverse Problems, 7 cr

Implementation MAT-62006 2018-01

Description

The course is aimed for students who need to solve inverse and ill-conditioned problems in their work. The participants will learn how to approach a numerical inverse problem in which the data can be predicted via an advanced mathematical forward model and a priori information is needed in finding the solution. In particular, they will learn about the following topics: (1) applications involving inverse problems, (2) forward modeling, (3) inversion methods, (4) statistical approach and prior models, and (5) computed examples (Matlab).

Language of instruction: English

Course code: MAT-62006

Discipline: Mathematics

Level of studies: Advanced. The course will be particularly useful for postgraduate-level students who apply mathematical modelling and imaging methodology in their work.

Prerequisites: Calculus courses, linear algebra basics, principles of ordinary and partial differential equations.

Working methods: This inverse problems course will consist of ten daily lectures, four exercise sessions, exam and a project work. The focus will be on numerical inverse problems which today arise in various fields of science and engineering including, for example, applied physics, biomedical and biological imaging, geophysics and signal processing. The emphasis will be on forward modelling, regularization approaches and statistical methods. Each lecture will consists of both theoretical viewpoints and computational examples. A careful demonstration of each example will be given in the exercise sessions. The methods will be also utilized in the project work. Matlab will be used as the programming platform.

Teacher responsible: Sampsa Pursiainen

Course material: Jari Kaipio and Erkki Somersalo, Statistical and Computational Inverse Problems, Springer, New York, 2004.

In questions concerning course content, please contact Sampsa Pursiainen: sampsa.pursiainen(at)tuni.fi

Lessons

Assessment scale

Numerical evaluation scale (0-5)

Requirements

Evaluation: Exam, exercises and project work

Study material