MATA2510 Introduction to Computational Inverse Problems (4 cr)

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


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 (
2. Jennifer Mueller, Samuli Siltanen: Linear and Nonlinear Inverse Problems with Practical Applications, 2012. (A supporting textbook, but not mandatory.)

Completion methods

Method 1

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

Participation in teaching (4 cr)

Participation in teaching
Grading scale:
English, Finnish
No published teaching