Head of Laboratory – Dr.Sc. (Mathematics) Boris Miller

Tel.: (095) 209-47-81; E-mail: bmiller@iitp.ru

The leading researchers of the laboratory include:

The investigations in the area of generalized solutions in the optimal control problems for impulsive stochastic control systems were continued. The equivalence of that problem and some convenient stochastic control problem with stopping time and bounded controls was proved. This result is a basis for derivation of the existence theorems and optimality conditions.

The representation problem for optical flow, generated by primitive flat motions like (shift, rotation, and stretching) was solved. This optical flow was represented with aid of affine system of differential equations. The Lie algebra of image transformations, which describes the evolution of transformation parameters was obtained. The aim of this work is creation of optimal compression algorithms for moving images.

The problem of observation control in system with noises dependent on estimation was considered. The solution existence theorem was proved. The aim of this work was the creation of the optimal control methods in systems with correlation measurements. One of possible application is the determination of motion parameters on the basis of video-sequences analysis.

We study the task of distorted image reconstruction with a priory known distortion (distort operator) in frame of the problem of unbounded operator restoration. In many cases this task can be reduced to the problem of numerical solution of 2D-convolution equation. We developed and realized the model for generating the distorted images with given type of distortion and distortion parameter values. The carried out mathematical experiments demonstrated, that if the distort operator was known explicitly, or could be enough closely approximated, and the noise level was low (the stochastic error was low), even the ordinary linear restoration algorithms gave the satisfactory results.

We developed and realized the base mathematical model of 2D Radon tomography. In the frame of the model we investigated the opto-acoustic tomography system for early diagnostic of breast cancer. The rough preliminary estimates for possible metrology characteristics of the system were obtain.

In a framework of project performed under the grant of Samsung Electronics (SAIT) the multi-level pyramidal hierarchial segmentation algorithm for color images was developed. The algorithm was realized as a S/W for PC. The results of work were adopted by SAIT.

A relational database was developed to be used as a template structure for representation of archival information stored in the Archive of RAS. Unlike widely known full-text databases, the structure is targeted primarily at archival collections of graphic data which have to be reproduced with authenticity (e.g. photographs, sketches, handwritten notes). In addition to was developed and published. It relies on the updated database and features also German language version. A Web site of the same name was re-developed accordingly. The site (http://hp.iitp.ru) works since July, 1998 and is being visited intensively. The developed generic structure of the text-and-graphics database for the Archive of RAS was applied to store an archival collection of medals (RAS Archive, Category XIII). Currently this database is being populated. It is logically linked to RAS2000 database, thus enriching the content of both databases.

In a framework of general problem "Restoration of blurred images" the novel nonlinear image restoration algorithms were developed. Some approaches to the problem of a posteriori determination of blurring operators were investigated. Particularly, the possibility to apply the modern recognition algorithms to identification of blurring operators and determination of the blurring parameters was also investigated. This investigation was based on amplitude component of the blurring operator spectrum in rather simple mathematical models.

For adaptation of the recognition algorithms to the solution of the problem the representative database was created.

On the basis of recursive relations the analytical properties of the amplitude-frequency and phase-frequency characteristics of two-rays radio-channels were investigated. These characteristics determines the stability of the stochastic information transmission systems with frequency, phase and amplitude modulation.

• The project of the State scientific and technical subprogram "Information of Russia" of priority direction of "Information technologies and electronics" (No. 037.03.319.17/1-99): "Development of integrated system for storage and processing multidimensional signals for information maintenance of scientific researches, culture and education", subpart "Development of technology and software for construction of multilevel text-graphic digital archives on the basis of conventional database management system" (jointly with Sector of Digital Optics).

1. Aizenberg I., Aizenberg N., Bregin T., Butakov C., Farberov E., Merzlyakov N., Milyukova O. Blur Recognition on the Neural Network based on Multi-valued Neurons // Proc. of First International Conference on Image and Graphics, August 16-18, 2000, Tianjin, China, p. 127-130.
2. Karnaukhov V.N., Merzlyakov N.S., Rubanov L.I. Integration of Image Processing and Database Management Systems // Proc. of the First International Conference on Image and Graphics, August 16-18, 2000, Tianjin, China, p. 665-668.
3. Karnaukhov V.N., Merzlyakov N.S., Milyukova O.P. Multi-functional digital model of the image blurring and restoration // Computer Optics. 2000. No. 20. P. 118-121.
4. Rubanov L.I., Karnaukhov V.N., Kuznetsov N.A., Merzlyakov N.S. Interactive Systems for Digital Processing, Storage and Displaying of Archival Images // Proc. of the 3rd International Conference "Digital Image Processing and its Application" (Moscow, November 29 – December 1, 2000), RNTORES – ICS RAS, p. 118-123.
5. Miller B.M. Observation Control for Discrete-Continuous Stochastic Systems // IEEE Trans. Automatic Control. 2000. V. 45. No. 5. P. 993-998.
6. Serebrovskii P.A. Investigation of the flat motion representations by methods of the differential equations theory. Master Thesis. Moscow Institute of Physics and Technology, 2000.