WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 12, 2016
3D Image Representation through Hierarchical Tensor Decomposition, Based on SVD with Elementary Tensor of size 2x2x2
Authors: Roumen Kountchev, Roumiana Kountcheva
Abstract: As it is known, groups of correlated 2D images of various kind could be represented as 3D images, which are mathematically described as 3rd order tensors. Various generalizations of the Singular Value Decomposition (SVD) exist, aimed at the tensor description reduction. In this work, new approach is presented for 3rd order tensor decomposition, where unlike the famous methods for decomposition components definition, iterative calculations are not used. The basic structure unit of the new decomposition is an elementary tensor (ET) of size 2ï‚´2ï‚´2, which builds the 3D tensors of size NÃ—NÃ—N, where N=2n. The decomposition of the single Ð•Ð¢ is executed by using Hierarchical 2-level SVD, where (in each level) the SVD of size 2Ã—2 (SVD2Ã—2) is applied on all sub-matrices obtained after the elementary tensor unfolding. The so calculated new sub-matrices of the SVD2Ã—2 in each hierarchical level, are rearranged in accordance with the lessening of their corresponding singular values. The computational complexity of the new tensor decomposition is lower than that of the decompositions, based on iterative methods, and permits parallel calculations for all SVD2Ã—2 for the sub-matrices in a given hierarchical level.
Keywords: 3D images, tensor decomposition, Hierarchical SVD (HSVD), elementary tensor of size 2x2x2
Pages: 210-218WSEAS Transactions on Signal Processing, ISSN / E-ISSN: 1790-5052 / 2224-3488, Volume 12, 2016, Art. #25