Third-Order Tensor Representation Through Reduced Inverse Difference Pyramid

Abstract

In this work is presented a method for the third-order tensor representation through Reduced Inverse Difference Pyramid. In each of the pyramid levels is used the 3D Walsh-Hadamard transform and as a result is achieved high concentration of the tensor energy in a minimum number of spectrum coefficients, most of which - in the first decomposition level. The tensor is thus transformed into multi-layer spectrum tensor of same size. The corresponding decomposition pyramid is not "overcomplete", and is called „reduced". The representation has minimum computational complexity because the only operation needed for the execution, is „addition". The evaluation of the pyramid properties opens new abilities for its application in various areas, aimed at the information redundancy reduction in multidimensional signals and data.