Inverse Problems (in Astrophysics)
by
Nikolai Piskunov
The remote sensing differs from
laboratory science by the fact that the object of study cannot be dissected or specially
prepared and the measured data is related in a complex way to the properties of
the target. The same is also true when the measuring procedure itself
influences the results. Both of these are true for research in
Astrophysics.
Plan (8 lectures + student seminars. Course completed by middle October
2014.)
During this course you will learn:
- How
information about target is related with the observations
- How
a remote sensing measurement can be described with an integral equation
- What
are the typical kinds of integral equations encountered
- What
are the problems related to solving integral equations
In the process of the course I will use selected astrophysical and
non-astrophysical examples to illustrate:
- How
to formulate a problem as in integral equation and to solve it using the
inverse problem techniques
- How
to choose an appropriate functional form and value of regularization
- How
to select the numerical method for solving an inverse problem
Literature:
Selected papers from e-journal
"Inverse Problems", ApJ and
A&A
Students will have to:
-
Do the home work consisting of making computer
codes reproducing examples described in class
-
Select on paper from the proposed list, study it
and present in the class
-
Formulate their own projects based on their area
of research and to solve them using suitable optimization techniques and
favorite programming language
-
Present the results in the class
in order
to pass the course. No exam!
Lectures:
mostly Tuesdays and Thursdays, 10:15, Celsiusrummet (6341)
Prof. Nikolai Piskunov
piskunov@astro.uu.se
tel: 018 471 59 58
Lecture
Notes and Exercises
Lecture 1 (Aug
28th, 10:15) Introduction to remote sensing as inverse problem
Lecture 2 (Sep
2nd, 10:15) History and the concept of an ill-posed problem
Lecture 3 (Sep
4th, 10:15) Regularization 1
Lecture 4 (Sep
9th, 10:15) Regularization 2
Lecture 5 (Sep
11th, 10:19) Finding regularized solution
Lecture 6 (Sep
16th, 10:15) Doppler Imaging
Lecture 7 (Sep
19th, 10:15) Parallel Computing
Some more hints about optimal filter exercise can be found here
Lecture 8 (Sep
23rd, 10:15) Concluding remarks