1. komponenta

Lecture type	Total
Lectures	45

COURSE AIMS AND OBJECTIVES:
This is an introductory course in inverse problems using techniques of statistical inversion theory. Prototype problems will be in image processing with tasks like image denoising, image reconstruction and such.

COURSE DESCRIPTION AND SYLLABUS:

1. Inverse problems and a model of measurement
2. Singular value decomposition
3. Randomised algorithms and low rank approximations
4. Convex optimisation
5. Sparse data representation
6. Regularization and LASSO
7. Bayesian inversion
8. Statistical inversion
9. Methods of deep learning
10. Fourier and Radon transform
11. Applications in image processing (Roentgen CT)

1. Statistical and Computational Inverse Problems, Jari Kaipio, Erkki Somersalo, Springer, 2005.
2. Inverse Problem Theory and Methods for Model Parameter Estimation, Albert Tarantola, http://www.ipgp.fr/~tarantola/Files/Professional/Books/InverseProblemTheory.pdf.
3. Introduction to Bayesian Scientific Computing, D. Calvetti, E. Somersalo, Springer, 2007.
4. Compressive Imaging: Structure, Sampling, Learning, Ben Adcock, Anders Hansen.

Izborni predmet 1, 2, 3 - Regular study - Mathematical Statistics

Izborni predmet 1, 2, 3 - Regular study - Mathematical Statistics

Izborni predmet 4, 5, 6, 7 - Regular study - Mathematical Statistics

Izborni predmet 4, 5, 6, 7 - Regular study - Mathematical Statistics