## Lecture on Information Theory & Information Field Theory

Imaging in astronomy, geology and medicine require intelligent methods to obtain high fidelity images from noisy, incomplete data. The theoretical and mathematical framework in which imaging and data analysis methods are derived should be information theory to which these lectures will introduce first (first 1/3 semester 09.04.18 - 11.5.18, suited for Bachelor and Master students, 3 ETCS). Based on this, information theory for fields will be developed, which can be used to reconstruct signals from data (remaining 2/3 semester, 14.05.18-13.7.2018 more targeted at Master students, 6 ETCS).

The following topics will be addressed:

- Aristotelian & Bayesian logic
- Measurement process
- Information measures
- Relation to thermodynamics and statistical mechanics
- Theory of Wiener filter
- Construction of optimal non-linear filters

**There will be two lectures per week
Information theory starts 09.04.2018 and ends 11.5.2018
Information field theory starts 14.05.18 and ends 13.07.2018:**

- Monday, 14:00- 16:00, Theresienstr. 37, A348
- Tuesday, 14:00- 16:00, Theresienstr. 39 - Arnold Sommerfeld (B 052)

**Examinations:
Information theory: Tuesday, 29.05.2018 14:00- 16:00 Theresienstr. 39, - Arnold Sommerfeld (B 052)
Information field theory: Monday, 9.7.2018 14:00- 16:00 Theresienstr. 41 - C 123
IFT 2018 examination results (preliminary)
**

## Tutorials for Information Theory & Information Field Theory

**There are three tutorials per week:**

- group A, Wednesday 16:00 - 18:00 room B 101, Theresienstr. 39
- group B, Wednesday, 8:00 - 10:00, room A 449, Theresienstr. 37
- group C, Thursday, 10:00 - 12:00, room A 449, Theresienstr. 37

## Bonus System

**If you like to take advantage of the bonus system you must register yourself via the button found above under the lecture description. **

Exercises are optional, but can be used to get bonus points for the exam. The bonus
will be 15% of the points which are necessary to achieve a 1.0 in the exam. The bonus
system is structured as following:

Each week we will hand out work sheets with approximately three problems. To each task and
subtask, respectively points are assigned. Prior to each tutorial students are asked to
give note which problems they may solve on the blackboard. Students need to sign up
for at least 60% of all possible achievable points during each part, IT and IFT, in order to
get the bonus for the respective exam. Besides this the tutors randomly choose students
to present their solutions of the work sheet on the black board. In case the student is
not able to properly solve the task, instead of getting the points for this exercise he/she
will receive up to twice the negative number of points he could have gained by the correct solution.
It will be ensured that top marks are well reachable without the bonus.

- Exercise sheet 1
- Exercise sheet 2
- Exercise sheet 3
- Exercise sheet 4
- Exercise sheet 5
- Exercise sheet 6
- Former IT examinations: 2015, 2016, 2017
- Info: The IT examination 2018 will cover the script up to Gaussian distributions (inclusive). Wiener filter and Optimal linear filter will not be part of it, but part of the IFT examination 2018.
- Exercise sheet 7
- Exercise sheet 8
- Exercise sheet 9
- Exercise sheet 10
- Exercise sheet 11
- Former IFT examinations: 2015, 2016, 2017 IFT 2018 examination results (preliminary)

## Seminar on Information Theory & Signal Reconstruction

The seminar is intended for participants of the lecture on Information Theory
(1/3 semester) & Information Field Theory (2/3 semester), the content of which will be
assumed to be known by all participants.
The main seminar goal is to extend the participants' knowledge beyond the material
covered in the lecture, especially
with respect to concrete measurement situations, imaging, and existing algorithms.
A second goal is to practice presentations and open discussions.
Talks can be given at the blackboard, or by using computer projection and should be in
English and of 10 minutes length, to be followed by a 10 min discussion.
**Topics must be coordinated with the seminar leaders (mainly with Torsten Enßlin, ensslin@mpa-garching.mpg.de and
Theo Steininger, theos@mpa-garching.mpg.de), no later than by June, 1st 2018.**
A pdf-file with slides or write-up of presented material (readable handwriting is ok)
must be provided by the student beforehand.
Computer presentations must be sent in via email to theos@mpa-garching.mpg.de on the day before the seminar,
so that they can be put on a single presentation computer.
A marked certificate for 3 ECTS points will be provided to any student who

- attends both of the seminar dates
- gave an acceptable talk
- and provided a pdf file with the talk slides or write-up to document her/his participation.

**The seminar will take place on two days:**

- Thursday, 21.06.2018 9am - 5pm, old lecture Hall, Max-Planck-Institute for Astrophysics in Garching
- Friday, 22.06.2018 9am - 5pm, old lecture Hall, Max-Planck-Institute for Astrophysics in Garching

Topics can be picked, or chosen according to the students own interests. The talks should

- make contact with the subject of the lecture
- capture the essential of its topic rather than try to be exhaustive
- extend the knowledge of the audience

Interesting topics can be found in the fields of :

- Numerical optimization (e.g. heavy ball methods, steepest descent, etc.)
- Medical imaging devices (e.g. computer tomography, nuclear magnetic resonance, etc)
- Astronomical imaging devices (e.g. optical telescopes, X-ray telescopes, CMB satellites, etc.)
- Geological probes (e.g. seismic waves, gravitational field measurements, etc.)
- Signal reconstruction/filter algorithms (e.g. Kalman filter, compressed sensing, audio/image compression, etc.)
- Specific signals (e.g. Cosmic Microwave background radiation, climate data, stock market price, etc.)
- Applications of theory (e.g. Game theory, weather forecast, insurance mathematics etc.)

If you would like to participate please register via the button found above under the lecture description.

It is expected that the students prepare the talks on their own, without supervision. If difficulties with a topic arise during the preparation (e.g. suitable literature cannot be found, topic is too difficult to be presented or too trivial to be interesting) the student should change the topic of the talk to circumvent the problem. If she/he decides for a complete change of the topic, the seminar leaders should be informed via email. Literature research is part of the preparation work of the student. Teamwork and splitting of topics into several coordinated talks is welcome. Students are encouraged to have test talks with co-students beforehand. Marks will be given according to the main criterion how informative the talk was given the lecture background. The quantity of presented material will be less important than the quality of the information transferred.