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- A. L. Reznik, V. M. Efimov, A. V. Torgov, A. A. Solov’ev
- Pattern Recognition and Image Analysis
- 2012

The novelty and originality of the presented studies consists of the fact that the rigorous mathematical proof of one of relationships that describe the probability of an error-free reading of random discrete images contained in them was previously found by the authors using specially created programs for computer analytical calculations.

- A. L. Reznik, V. M. Efimov, A. A. Solov’ev, A. V. Torgov
- Pattern Recognition and Image Analysis
- 2015

An original approach is proposed to solve rather complex probabilistic problems of the readout of random discrete-point fields; these problems lack an exact analytical solution. Schemes are proposed for the direct, iterative, and combinatorially recursive analytical calculation of multidimensional integral expressions that describe the partial solutions of… (More)

- A. L. Reznik, A. A. Solov’ev, A. V. Torgov
- Pattern Recognition and Image Analysis
- 2016

Original programming, combinatorial, and geometric schemes are presented. They have been developed and used by the authors to calculate exact analytical formulas that describe the probability of the formation of local groups of a given size in random point images. Formulas, which will be discussed below, arise in the assessment of the reliability detection… (More)

- A. L. Reznik, V. M. Efimov, A. V. Torgov, A. A. Solov’ev
- Pattern Recognition and Image Analysis
- 2011

The novelty and originality of the presented studies consist in a rigorous mathematical proof of one of the relationships describing the probability of correct reading of a random discrete image. The proved assertion was obtained earlier by the authors with the use of specially developed programs for analytic computations.

- V. M. Efimov, A. L. Reznik, A. V. Torgov, A. A. Solov’ev
- Pattern Recognition and Image Analysis
- 2012

A way to use an algorithm for compensating for linear distortions for solving a set of linear algebraic equations with a band matrix is examined. The relationships needed for step-by-step finding of a solution are generated, and the framework in which the relationships are correct is determined.

- V. M. Efimov, A. L. Reznik, A. V. Torgov
- Pattern Recognition and Image Analysis
- 2007

The effect of the bias in a sequence of signal samples and sequence of signal derivative samples on the signal reconstruction accuracy is considered for a bandwidth-limited signal.

- V. M. Efimov, A. L. Reznik, A. V. Torgov, A. A. Solov’ev
- Pattern Recognition and Image Analysis
- 2011

The possibilities of the application of a linear distortion compensation algorithm in solving the systems of linear algebraic equations with band matrices are considered. The relationships required for the step-by-step solution procedure are derived, and the conditions of their correct application are determined.

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