3D Image Representation through Hierarchical Tensor Decomposition, Based on SVD with Elementary Tensor of size 222

As it is known, groups of correlated 2D images of various kind could be represented as 3D images, which are mathematically described as 3 rd 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 3 rd 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 222, which builds the 3D tensors of size N×N×N, where N=2 n . The decomposition of the single ЕТ is executed by using Hierarchical 2-level SVD, where (in each level) the SVD of size 2×2 (SVD2×2) is applied on all sub-matrices obtained after the elementary tensor unfolding. The so calculated new sub-matrices of the SVD2×2 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 SVD2×2 for the sub-matrices in a given hierarchical level. Key-Words: 3D images, tensor decomposition, Hierarchical SVD (HSVD), elementary tensor of size 222.