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Filtering efficiency of random fields with multiple roots of characteristic equations

Keywords:

K.K. Vasilev – Dr.Sc.(Eng.), Professor, Head of Department «Telecommunications», Ulyanovsk State Technical University
E-mail: vkk@ulstu.ru
N.A. Andriyanov – Ph.D.(Eng.), Programmer, Department «Telecommunications», Ulyanovsk State Technical University
E-mail: nikita-and-nov@mail.ru
Kh.A. Abdulkadim – Ph.D.(Eng.), Lecturer, Department «Communication Engineering», University of Diyala (Iraq)
E-mail: hussein73@mail.ru


The disadvantages of the simplest autoregressive models of multidimensional images include the pronounced anisotropy of generated random fields (RF). At the same time, the use of separable causal models formed by autoregressions with multiple roots of the cha-racteristic equations makes it possible to approximate the realization of such RFs to isotropic fragments of real multizone images. In connection with this, problems arise in the study of the properties of these RFs, some of which are solved in the present paper. In particular, it is necessary to investigate the probabilistic characteristics of imitated images. This in the future will allow an adequate substitution of real images for simulated ones. In addition, in this paper we investigate the filtering efficiency of simulated RF. Knowledge of the minimum achievable error variances for various parameters when processing real images can help determine whether it is expedient in this situation to use a filter based on the model under study.
A lot of real images have fairly smooth brightness differences. The known autoregressive models of random fields (RF) either do not adequately describe such images even with strong correlation (first order), or require rather complex operations to calculate the set of correlation parameters (with increasing order). Meanwhile, autoregressive RF models are known, and they are generated by the characteristic equations. Such models are called autoregressions with multiple roots. At the same time, the use of algorithms based on such models, when processing real images and in various applied problems, can improve the efficiency of solving such problems.
Among them, the important task is to suppress noise or filter images, the solution of which is often found with the help of recurrent algorithms and based on the calculation of the covariance filter error matrix. However, transformations used in this approach can sig-nificantly increase the time spent on solving this problem. To find the efficiency of the optimal filter, it is necessary to use the Wiener-Hopf equations. Thus, the problem of investigating the correlation properties of autoregressions with multiple roots of characteristic equations, as well as the problem of optimal filtration of RF generated by such models, are of particular interest.
The article gives a rather complete description of autoregressive models with multiple roots of characteristic equations. In the paper, the correlation coefficients for the models of different orders are obtained from the correlation interval, which is equal for all models.
An optimal RF filter generated by autoregressive models of various multiplicity is also considered. On the example of models of the first and second orders, a comparative analysis of the efficiency of filtration is performed. Dependences of dispersion of the filtration error on the correlation interval of the model along the axes for different signal-to-noise ratios are found.
Thus, in the article autoregressive models with multiple roots of characteristic equations are considered. It is shown that an increase in the order of the model leads to an increase in filtration efficiency.

References:
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  3. Vasilyev K.K., Popov O.V. Autoregression models of random fields with Multiple Roots // Pattern recognition and Image analysis.1999. V. 9. № 2. P. 327−328.
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June 24, 2020
May 29, 2020

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