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



   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

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