Use of symmetric Hadamard and Mersenne matrices in digital image processing

Vostrikov, Anton A.; Sergeev, Mikhail; Балонин, Н. А.; Sergeev, A.

doi:10.1016/j.procs.2018.08.042

Cited by 9 publications

(4 citation statements)

References 12 publications

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“…Матрицы Адамара и подобные им квазиортогональные матрицы применяются в обработке сигналов и изображений [13,16,23], помехоустойчивом кодировании изображений [18], в кодировании [9] и многих других технических задачах. В целом результаты наших поисков показали способность новых подходов при разработке алгоритмов давать значительный результат.…”

Section: матрицы адамара и области их примененияunclassified

Improving the efficiency of Hadamard matrix mining for digital conversion methods

Balonin¹,

Vostrikov²,

Kurtianik³

et al. 2022

Proceedings of II All-Russian Scientific Conference "Science, Technology, Society"

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. The problem of searching for Hadamard matrices is considered as mining, which includes setting initial conditions, choosing matrix designs, and "enriching" a set of sequences through filtering the Fourier spectra of sequences. Mining difficulties are analyzed and a way to overcome them is considered. Examples of the choice of the Propus design, pre-filtering of the generated sequences to speed up calculations are given.

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Section: матрицы адамара и области их примененияunclassified

Improving the efficiency of Hadamard matrix mining for digital conversion methods

Balonin¹,

Vostrikov²,

Kurtianik³

et al. 2022

Proceedings of II All-Russian Scientific Conference "Science, Technology, Society"

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Section: матрицы адамара и области их примененияunclassified

“…Надежность программного обеспечения определяется как вероятность безотказной работы программного обеспечения в течение заданного периода времени в заданной среде [23]. Отказы любого продукта возникают из-за сбоев или наличия Для достижения поставленной цели решаются следующие задачи:…”

Section: анализ взаимосвязи надежности по и транзакционной структурыunclassified

Proceedings of II All-Russian Scientific Conference "Science, Technology, Society"

2022

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“…Mathematical objects, such as matrices with small number of their element values (levels), are corresponded by determinant-extreme solutions which find practical use in image processing and noise-immune coding problems [1,2], such as impulse-noise-resistant coding of images transferred via telecommunication channels [3], formation of nested code structures based on Barker codes with improved auto-correlation functions [4], image transformation for better protection from unauthorized use [5], etc.…”

Section: Introductionmentioning

confidence: 99%

The rise in maximum determinant matrix complexity

Vostrikov

Balonin

Sergeev

2021

ICS

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Introduction: In spite of the apparent relation between maximum determinant matrices of even (Hadamard matrices) and odd orders, the latter have particularly complex patterns of repetitive elements. This is what makes them unique and attractive for various applications in visual data processing, coding and masking. Purpose: Developing the theory of maximum determinant matrices, with the focus on using computer-aided analysis, and calculating unique matrices with unique pattern structures in their portraits. Results: We have found some peculiarities of maximum determinant matrices, outlined their families related to Fermat numbers, demonstrated the complication of patterns in other matrices as their orders grow. The presumption about the increasing complexity of structures as the matrix orders grow is confirmed by a chain of matrix portraits we demonstrate. As applied to orthogonal Belevitch matrices, it follows that they cannot be found even in small orders such as 66 or 86.

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Use of symmetric Hadamard and Mersenne matrices in digital image processing

Cited by 9 publications

References 12 publications

Improving the efficiency of Hadamard matrix mining for digital conversion methods

Improving the efficiency of Hadamard matrix mining for digital conversion methods

Proceedings of II All-Russian Scientific Conference "Science, Technology, Society"

The rise in maximum determinant matrix complexity

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