Autors: Кунчева Р. А., Mironov, R. P., Kountchev, R. K.
Title: MLTSP: New 3D Framework, Based on the Multilayer Tensor Spectrum Pyramid
Keywords: tensor decomposition; multilayer tensor spectrum pyramid; 3D orthogonal transform; hierarchical tensor SVD; 3D modified Mellin–Fourier transform

Abstract: A tensor representation structure based on the multilayer tensor spectrum pyramid (MLTSP) is introduced in this work. The structure is “truncated”, i.e., part of the high-frequency spectrum coefficients is cut-off, and on the retained low-frequency coefficients, obtained at the output of each pyramid layer, a hierarchical tensor SVD (HTSVD) is applied. This ensures a high concentration of the input tensor energy into a small number of decomposition components of the tensors obtained at the coder output. The implementation of this idea is based on a symmetrical coder/decoder. An example structure for a cubical tensor of size 8 × 8 × 8, which is represented as a two-layer tensor spectrum pyramid, where 3D frequency-ordered fast Walsh–Hadamard transform and HTSVD are used, is given in this paper. The analysis of the needed mathematical operations proved the low computational complexity of the new approach, due to a lack of iterative calculations. The high flexibility of the structure in



    MDPI Symmetry, vol. 14, issue 9, pp. 1909, 2022, Switzerland, MDPI, ISSN:20738994, DOI: 10.3390/sym14091909

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