Referee report 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”  Diploma work which is presented for defense is devoted to a comparative analysis of astronomical images processing methods and their application for studying the various objects contained in these images. The actuality of this trend is directly linked to the intensive development of astronomical equipment. Modern CCD matrixes contain up to several hundreds of millions of pixels. In result of observations the matrix detects the radiation of objects of different brightness and at different distances from the observer which are located in a large volume of space. In a projection a complex two-dimensional pattern on the plane  is formed, where the radiation from different objects can be overplotted. The noise contribution can pollute the image. Decoding the information contained in these images and the decomposition of the plot on the individual components, which is important for investigators, is a quite difficult problem.  There are many modern mathematical methods of processing and analysis of two-dimensional images already exists. They can be divided into two categories: the spatial and the frequency. The former includes various kinds of filtering on the so-called masks, which uses the linear and non-linear as well as the low and high frequency filters. The various types of Fourier and wavelet transforms are the frequency processing methods. The author of the diploma work presents a detailed overview of the various processing methods, performs a comparative analysis of their effectiveness, which is demonstrated for model images. He has shown the advantage of multi-level wavelet transform in a comparison with the older standard methods of filtration. Numerous examples of the use of these methods are provided in the main text of the thesis, as well as in several appendixes. Noteworthy, the author independently developed the computational algorithms and wrote specific programs of calculations. Special attention was attract to the use of multi-level wavelet analysis methods to identify clusters in the images of galaxies and to the search for individual objects with the specified characteristics. As a specific example, this technique has been used to search the young clusters and finding their relations with bright blue variables (LBV- stars). It has been shown that the spatial distribution of the clusters relatively LBV- stars is not random. This result can serve as a confirmation of the hypothesis that LBV-stars can be kicked from the stellar clusters in the early stages of their formation. The diploma work is written by good scientific language and well arranged, although it contains a number of typos. It should also be noted that detailed descriptions of the mathematical transforms, which are familiar to those skilled in the field, are not clear for the other readers. They should be accompanied by appropriate comments in a language accessible to a wider range of researchers interested in this topic. A number of intermediate values and concepts found in the text, require a separate explanation. Many results which are presented in the diploma can be recommended for publication. I believe that the diploma work by A.E.Kostenkov deserves an EXCELLENT mark.   Chief Researcher, Pulkovo observatory, Dr . M.A.Pogodin May 23, 2016  Signature of M.A.Pogodin assure: 				          Scientific secretary  of Pulkovo observatory, Phd. T.P.Borisevich