A one-day doctoral course on Regularization Methods for Discrete Inverse Problems will be held by Dr. Silvia Gazzola, Department of Mathematical Sciences, University of Bath, on Thursday, September 21, 2023.
Course description:
Inverse Problems arise in many Engineering and Scientific applications. Because of their inherent ill-posedness, solving inverse problems is always a delicate task and appropriate regularization methods should be employed for this purpose. This course will introduce you to a variety of popular regularization methods that can be used when solving large-scale linear inverse problems. Specifically, topics to be addressed include:
- Singular value decomposition of a matrix as a tool for analyzing linear inverse problems
- Popular spectral filtetring methods, such as Tikhonov regularization
- Popular iterative regularization methods for linear systems, such as Landweber method, CGLS and LSQR
- Strategies for choosing the regularization parameter
- Applications to inverse problems in computed tomography
The course will comprise a mixture of theoretical lectures and practical exercises, aimed at giving you insight into the workings of the most common regularization methods. The practical part will be based on IR Tools, which is a MATLAB Package of Iterative Regularization Methods and Test Problems for Linear Inverse Problems.
IR Tools is available through github: https://github.com/jnagy1/IRtools.
You can learn more about IR Tools by visiting the page: http://people.compute.dtu.dk/pcha/IRtools/.
Prerequisite for the course are a basic background on numerical linear algebra, access to MATLAB, and a basic familiarity with MATLAB.
The course material will largely be based on the following resources:
[1] Per Christian Hansen, Discrete Inverse Problems, Society for Industrial and Applied Mathematics, 2010. epubs.siam.org/doi/abs/10.1137/1.9780898718836
[2] Julianne Chung and Silvia Gazzola, Computational methods for large-scale inverse problems: a survey on hybrid projection methods https://arxiv.org/abs/2105.07221
Time schedule:
Location: Inffeldgasse 25/F, Ground Floor, 8010 Graz
| 09:00 - 12:00 |
Classical filtering and iterative methods for linear problems |
| 12:00 - 13:00 |
Lunch at Mensa on the Campus |
| 13:00 - 17:00 |
Towards state-of-the-art solvers for inverse problems |
There will be a morning and afternoon break with refreshments.
On the evening before (Wednesday, September 20, 2023, 7:00 pm) all participants of the course are cordially invited to a dinner together.
Location: "Bar 28", Gartengasse 28, 8010 Graz
