MATA2510 Introduction to Computational Inverse Problems (4 cr)
Description
CONTENT
Matlab programming, discerete convolution and deconvolution, Hadamard's conditions of well-posedness, minimum norm solutions, singular value decomposition (SVD) and condition number, Moore-Penrose pseudoinverse, truncated SVD, Tikhonov regularization
COMPLETION METHODS
An exam and completing an online course. Self-study based on an online material and online exercises. Optional weekly computer classes.
ASSESSMENT DETAILS
The final grade is based on an exam and success at the online course.
Learning outcomes
After the course student
- Understands discerete convolution as a matrix model
- Learns least-squares solution technique and see that it can be numerically unstable
- Shows how to use SVD to detect ill-posedness in a matrix-based inverse problem
- Understands why deconvolution needs special regularised methods
- Knows how to write robust Matlab algorithms for signal deconvolution and image deblurring
Description of prerequisites
Linear Algebra and Geometry 2, Vector calculus 1, basic programming skill is helpful but not mandatory
Study materials
1. The open MOOC-course of the University of Helsinki: Introduction to Computational Inverse Problems (mooc.helsinki.fi).
2. Jennifer Mueller, Samuli Siltanen: Linear and Nonlinear Inverse Problems with Practical Applications, 2012. (A supporting textbook, but not mandatory.)