Book Chapter10.1007/978-3-319-19830-9_13
Mersenne-Walsh Matrices for Image Processing
N. A. Balonin,Anton A. Vostrikov,Mikhail Sergeev,Mikhail Sergeev +3 more
- 01 Jan 2015
- pp 141-147
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TL;DR: In this article, a modified Paley method is presented for the calculation of Mersenne matrices at order values equal to odd prime numbers, allowing for calculation of the complete set of functions.
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Abstract: This paper presents a modified Paley method for calculation of Mersenne matrices at order values equal to odd prime numbers Some examples of Mersenne matrix sorting, allowing for calculation of the complete set of functions, are also considered A comparison of Walsh and Mersenne-Walsh systems of functions in terms of their properties and fields of application is provided The efficiency of this topic for use in the development of band-pass filters is indicated
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Citations
Compression and coding of images for satellite systems of Earth remote sensing based on quasi-orthogonal matrices
Ekaterina A. Kapranova,Vadim A. Nenashev,Mikhail Sergeev +2 more
- 09 Oct 2018
TL;DR: One of the ways to solve the problem of high-quality image processing with high resolution is the creation and use of new compression filters, new algorithms of noise-resistant coding, based on the use of orthogonal and quasi-orthogonal matrices of large sizes.
15
Distributed matrix methods of compression, masking and noise-resistant image encoding in a high-speed network of information exchange, information processing and aggregation
Ekaterina A. Kapranova,Vadim A. Nenashev,Alexander Sergeev,Dmitry A. Burylev,Sergey A. Nenashev +4 more
- 12 Nov 2019
TL;DR: The results of the search and formation of orthogonal bases, the methods of synthesis of quasi-orthogonal matrices for image processing problems that meet the formulated requirements are presented and the mechanisms for finding new classes of matrices allow creation and development of competitive methods of storage, presentation, compression, noise-resistant coding of data during their transmission in wireless high-speed networks of exchange, processing and aggregation.
12
Calculating symmetrical Hadamard matrices of Balonin-Seberry construction for coding and masking
TL;DR: The results of this work can be a starting point for developing new approaches to search for symmetric Hadamard matrices used in noise-immune coding and filtering of radio signals, masking and compression of digital images, and other applied telecommunication problems.
4
Portraits of Orthogonal Matrices as a Base for Discrete Textile Ornament Patterns.
Alexander Sergeev,Mikhail Sergeev,Anton A. Vostrikov,Daniil Kurtyanik +3 more
- 01 Jan 2019
TL;DR: This work proposes to use computationally difficult unique matrices with two features, namely, orthogonality and symmetry, to generate "portraits" of orthogonal matrices as unique rapports for creating ornament patterns.
3
Digital masking using Mersenne matrices and their special images
TL;DR: The security issues of digital images transferred via open networks and ensuring their confidentiality by a way of using a matrix masking method is considered, as well as examples of “portraits” of special images for Mersenne matrices.
3
References
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TL;DR: In this article, the authors studied a new closed set of functions normal and orthogonal on the interval (0, 1) for the interval 0 5 x 5 1, where each function takes only the values + 1 and − 1, except at a finite number of points of discontinuity, where it takes the value zero.
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Generalized Mersenne matrices and Balonin’s conjecture
TL;DR: The fundamental differences between the matrices of Mersenne and Fermat, which explain the failure of the proof of the Hadamard conjecture, are shown.
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