**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