MAT-62007 Inverse Problems, 5 cr

Additional information

Suitable for postgraduate studies. The implementation will not be executed during the academic year 2019-2020.

Person responsible

Mikko Kaasalainen


Implementation Period Person responsible Requirements
MAT-62007 2019-01 - Mikko Kaasalainen

Learning Outcomes

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 Core content Complementary knowledge Specialist knowledge
1. Singular value decomposition of a matrix and solution by SVD truncation. Classical and generalized Tikhonov regularization.     
2. Total variation regularization with emphasis on implementation issues.     
3. Regularization using truncated iterative solvers.     
4. Introduction to statistical (Bayesian) inversion. Theory and implementation of Monte Carlo Markov Chain methods.     
5. Practical applications: inverse problems of generalized projections     


Course Mandatory/Advisable Description
MAT-60000 Matriisilaskenta Mandatory    
MAT-60006 Matrix Algebra Mandatory    

Correspondence of content

There is no equivalence with any other courses

Updated by: Ullgren Sini, 10.04.2019