Inverse Problems (5cr)

Objective

The student will gain understanding of basics of the theory of linear inverse problems and will be able to utilize the theory in computational inverse problems in practical applications. The course develops the following generic skills: digitalization, critical thinking, identification and development of one's own expertise, and interaction and communication.

Content

- Introduction. - Basics of linear functional analysis - Singular value decomposition and pseudoinverse. - Tikhonov regularization. - Non-linear inverse problems. - Statistical interpretation of Tikhonov regularization. - Iterative methods.

Qualifications

Recommendations of the prior learning: differential calculus, matrix calculus and linear algebra, Matlab programming

Materials

Lecture notes

Further information

Time: The course will be held only every second academic year. You can see the course implementations in Study guide, under "Course Units" or "Show past courses". This course is intended for the following student groups: - Undergraduate students in Technical Physics (MSc) - Undergraduate students in Applied Physics (MSc) - Graduate students in technology, physics and mathematics.

Execution methods

Lectures 34 h, Exercises 16 h. Independent study 88h

Accomplishment methods

Modes of study: Exercises (40% mandatory) and examination or general examination. In a Finnish-language programme, a student has the right to use Finnish in both written and oral attainments. Evaluation criteria: Exercises pass-fail, examination 0-5 (approved performance 50% of the maximum points of the exam).