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Ruprecht-Karls-Universität Heidelberg Statistics of inverse problems Research Group Lecture course Statistics of inverse problems (SS 2023)
german english


Time and location
Exercises groups
Lecture outline
References Last edited on
2023/07/14 by jj.
Time and location of the lecture course:
Wednesday 09:15-10:45 and Friday 09:15-10:45, MΛTHEMΛTIKON, INF 205, SR 5
Please register by using Müsli to receive timely announcements about the lecture by email.

Contact:
Lecturer: Prof. Dr. Jan JOHANNES <johannes[at]math.uni-heidelberg.de>
Questions, please directly by email or by using the contact form.

Language:
The lecture will be given in English if there is at least one non-German speaking participant.

Exercise group:
Please register for the exercise group of Statistics of inverse problems by using Müsli
to obtain further details by eMail.
We propose the following exercise group:

DayTime MΛTHEMΛTIKON (INF 205)
Thursday 14:00 - 16:00 Seminarraum 5

Lecture outline:
The outline of the lecture (sections §01-§11, 07/06/2023) is published before the lecture takes place. All lecture notes can be found as soon as possible after the lecture separately on here as well as combined Part A (Le01-Le09), Part B (Le10-Le18) and Part C (Le19-Le24). In the following table the individual documents are ordered by subjects.
      outline note
Chap 1 Statistical inverse problems
§01 Noisy image and known operator le00 le01 le02 le03
§02 Noisy image and noisy operator le04 le05
Chap 2 Regularisation of inverse problems
§03 Ill-posed inverse problems
§04 Regularisation by orthogonal projection le06
§05 (Generalised) linear Galerkin approach le07 le08-le09
§06 Spectral regularisation le10
Chap 3 Regularised estimation
§07 Regularisation by orthogonal projection le11 le12 le13 le14
§08 (Generalised) linear Galerkin approach le15 le16 le17 le18
§09 Spectral regularisation le19
Chap 4 Minimax optimal estimation §01-§11 (07/06/2023)
§10 Minimax theory: a general approach
§11 Deriving a lower bound le20 le21
Chap 5 Data-driven estimation

References:
Comte: Estimation non-paramétrique. (Spartacus-idh, Paris, 2015)
Giné and Nickl: Mathematical foundations of infinite-dimensional statistical models. (Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 2016)
Engl, Hanke and Neubauer: Regularization of inverse problems. (Kluwer Academic, Dordrecht, 2000)
Klenke: Wahrscheinlichkeitstheorie. (Springer Spektrum, 3., überarbeitete und ergänzte Auflage, 2012.)
Kress: Linear integral equations (Volume 82 of Applied Mathematical Sciences. Springer, New York, 2 edition, 1989)
Tsybakov: Introduction to nonparametric estimation. (Springer Series in Statistics. Springer, New York, 2009)
Werner: Funktionalanalysis. (Springer-Lehrbuch, 6. Aufl. Springer Berlin Heidelberg New York, 2007)
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