# MATA2510 Introduction to Computational Inverse Problems (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

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

## Learning outcomes

After the course student
• Understands discrete 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.)

## Completion methods

### Method 1

Description:
An exam and completing an online course. Self-study based on an online material and online exercises. Optional weekly computer classes.
Evaluation criteria:
The final grade is based on an exam and success at the online course.
Select all marked parts
Parts of the completion methods
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### Participation in teaching (4 cr)

Type:
Participation in teaching