Autors: Kountchev, R. K., Mironov, R. P., Kountcheva R.
Title: Hierarchical Cubical Tensor Decomposition through Low Complexity Orthogonal Transforms
Keywords: decomposition of 3D cubical tensor; hierarchical 3D Fast Walsh-Hadamard Transform (3D-FWHT); 3D Hierarchical Fast Complex Walsh-Hadamard Transform (3D-FCHT)

Abstract: In this work, new approaches are proposed for the 3D decomposition of a cubical tensor of size N×N×N for N=2n through hierarchical deterministic orthogonal transforms with low computational complexity, whose kernels are based on the Walsh-Hadamard Transform (WHT) and the Complex Hadamard Transform (CHT). On the basis of the symmetrical properties of the real and complex Walsh-Hadamard matrices are developed fast computational algorithms whose computational complexity is compared with that of the famous deterministic transforms: the 3D Fast Fourier Transform, the 3D Discrete Wavelet Transform and the statistical Hierarchical Tucker decomposition. The comparison results show the lower computational complexity of the offered algorithms. Additionally, they ensure the high energy concentration of the original tensor into a small number of coefficients of the so calculated transformed spectrum tensor.



    MDPI Symmetry, vol. 12, issue 5, pp. 864, 2020, Switzerland, MDPI, ISSN 2073-8994

    Цитирания (Citation/s):
    1. Yasmin M. Alsakar, Nagham E. Mekky , Noha A. Hikal , Detecting and Locating Passive Video Forgery Based on Low Computational Complexity Third-Order Tensor Representation, J. Imaging 2021, 7(3), 47, MDPI, Basel, Switzerland. - 2021 - в издания, индексирани в Scopus или Web of Science
    2. P Petrov, V Georgieva, Vision-Based Line Tracking Control and Stability Analysis of Unicycle Mobile Robots, New Approaches for Multidimensional Signal Processing, pp 83-98, 2021, Springer. - 2021 - в издания, индексирани в Scopus или Web of Science

    Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus