Review on the graduate thesis of the student of the Astronomical department of Mathematics and Mechanics Faculty of St. Petersburg State University 
Kostenkov Alexander Evgenievich 
“An Analysis of Two-Dimensional Astronomical Images by Methods of Fourier and Wavelet Analysis”

Graduate thesis (diploma work) by A.E. Kostenkov devoted to the development of methods of an analysis of two-dimensional images and their decomposition on the details of various scales, as well as the use of these methods to analyze the astronomical images.
In the diploma a mathematical apparatus of Fourier and wavelet analysis and other methods of image analysis are presented and the theory of multi-level representation in astronomy is described. The efficiency of different methods of the image decomposition techniques is demonstrated for the model 2d plots. A comparison of results obtained by different methods is given.
The main part of the work is based on using the methods of wavelet analysis to identify stellar clusters and on the adaptive search of objects in images. With this approach the stellar clusters in the galaxy M33, which may be associated with the LBV-stars, were detected. The distribution of distances of LBV-stars to the stellar clusters was analyzed.  An evolution connection between LBV-star and clusters was statistically proven. Noteworthy that the methods developed by Kostenkov can be applied for the analysis of the images in other galaxies of the Local Group.
The diploma is well executed. In this work the modern approaches to the analysis of two-dimensional images are used. The important results which are essential for understanding the nature of LBV-stars in the galaxies of the Local Group were obtained. The results of the diploma can be published in a future.
I suppose that the diploma work by A.E. Kostenkov can be marked as EXCELLENT.

Scientific adviser,
Professor, Department of Astronomy,
St. Petersburg State University	 



A.F.Kholtygin