DSpace Collection:http://hdl.handle.net/20.500.12258/522020-04-05T12:32:47Z2020-04-05T12:32:47ZThe application of modular arithmetic for matrix calculationsKuchukov, V. A.Кучуков, В. А.Babenko, M. G.Бабенко, М. Г.http://hdl.handle.net/20.500.12258/119112020-03-24T15:06:54Z2019-01-01T00:00:00ZTitle: The application of modular arithmetic for matrix calculations
Authors: Kuchukov, V. A.; Кучуков, В. А.; Babenko, M. G.; Бабенко, М. Г.
Abstract: The article considers the application of the Residue Number System (RNS) for matrix calculations. This can be useful to improve the performance and reliability of calculations in digital signal processing and artificial neural networks. We have reviewed the algorithms for calculating the scalar product. Their modeling and comparison with the standard means of the NumPy library of the Python are carried out. Methods of translation between the positional numeral system and RNS are described and simulated. Conclusions about the applicability of methods for calculations on Python are made. We have present the fault-tolerant scheme for error detection and correction. The examples of error occurrence and their correction by the presented scheme are considered2019-01-01T00:00:00ZAnalysis of the quantization noise in discrete wavelet transform filters for 3D medical imagingChervyakov, N. I.Червяков, Н. И.Lyakhov, P. A.Ляхов, П. А.Nagornov, N. N.Нагорнов, Н. Н.http://hdl.handle.net/20.500.12258/119102020-03-24T14:58:02Z2020-01-01T00:00:00ZTitle: Analysis of the quantization noise in discrete wavelet transform filters for 3D medical imaging
Authors: Chervyakov, N. I.; Червяков, Н. И.; Lyakhov, P. A.; Ляхов, П. А.; Nagornov, N. N.; Нагорнов, Н. Н.
Abstract: Denoising and compression of 2D and 3D images are important problems in modern medical imaging systems. Discrete wavelet transform (DWT) is used to solve them in practice. We analyze the quantization noise effect in coefficients of DWT filters for 3D medical imaging in this paper. The method for wavelet filters coefficients quantizing is proposed, which allows minimizing resources in hardware implementation by simplifying rounding operations. We develop the method for estimating the maximum error of 3D grayscale and color images DWT with various bits per color (BPC). The dependence of the peak signal-to-noise ratio (PSNR) of the images processing result on wavelet used, the effective bit-width of filters coefficients and BPC is revealed. We derive formulas for determining the minimum bit-width of wavelet filters coefficients that provide a high (PSNR ≥ 40 dB for images with 8 BPC, for example) and maximum (PSNR = ∞ dB) quality of 3D medical imaging by DWT depending on wavelet used. The experiments of 3D tomographic images processing confirmed the accuracy of theoretical analysis. All data are presented in the fixed-point format in the proposed method of 3D medical images DWT. It is making possible efficient, from the point of view of hardware and time resources, the implementation for image denoising and compression on modern devices such as field-programmable gate arrays and application-specific integrated circuits2020-01-01T00:00:00ZA division algorithm in a redundant residue number system using fractionsChervyakov, N. I.Червяков, Н. И.Lyakhov, P. A.Ляхов, П. А.Babenko, M. G.Бабенко, М. Г.Lavrinenko, I. N.Лавриненко, И. Н.Deryabin, M. A.Дерябин, М. А.Lavrinenko, A. V.Лавриненко, А. В.Nazarov, A. S.Назаров, А. С.Valueva, M. V.Валуева, М. В.http://hdl.handle.net/20.500.12258/119092020-03-24T14:49:13Z2020-01-01T00:00:00ZTitle: A division algorithm in a redundant residue number system using fractions
Authors: Chervyakov, N. I.; Червяков, Н. И.; Lyakhov, P. A.; Ляхов, П. А.; Babenko, M. G.; Бабенко, М. Г.; Lavrinenko, I. N.; Лавриненко, И. Н.; Deryabin, M. A.; Дерябин, М. А.; Lavrinenko, A. V.; Лавриненко, А. В.; Nazarov, A. S.; Назаров, А. С.; Valueva, M. V.; Валуева, М. В.
Abstract: The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach2020-01-01T00:00:00ZMethods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target DistributionPavlenko, E. N.Павленко, Е. Н.http://hdl.handle.net/20.500.12258/119082020-03-24T14:35:09Z2020-01-01T00:00:00ZTitle: Methods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target Distribution
Authors: Pavlenko, E. N.; Павленко, Е. Н.
Abstract: The paper discusses the solution of the assignment task between two groups of mobile (MR) objects. The assignment task is to determine the purpose of MR to each other when playing football. This article analyzes well-known works devoted to the tasks of assignments, and the relevance of research in this area is noted. The task of target distribution is successfully solved with a small degree of uncertainty. The urgency of further research to solve the problem of target distribution in conditions of uncertainty is substantiated. The model of target assignment is considered. The basis of the model is a bipartite graph. The vertices of a bipartite graph are defined by the properties of MR. One group of MR is assigned red color and the other one group is blue. The properties of the mobile objects are formally determined by the membership grades given by the experts. Identification of a bipartite graph is a solution to the assignment problem. When the problem of target distribution on a bipartite graph is solved, the criterion of the maximum degree of bipartite is applied. Formulas are given to determine the degree of bipartite, taking into account the number of vertices in the graph and the weight of each edge in two fractions of the graph. The study of the target distribution model was carried out by the simulation method. A program is developed to solve the problem of assignments. Properties and degrees of belonging of properties of red and blue MR are set for carrying out researches. The program allows you to produce research and under equality of red and blue MR, and under their inequality. The analysis of modeling results is carried out2020-01-01T00:00:00Z