Circulant Euler-Jacket Transform and Its Applications Based on Fast Algorithm

Abstract

Motivated by the elegant characteristics of the Euler theorem, we propose a novel Euler-Jacket matrix. This matrix has a circle-limitation for exponential function and thus can be created by using matrix operations with angle information. Especially, the inverses of the yielded matrices equals the transpose of elements inverse. It corresponds to the polynomial function, which is an unit operation of the orthogonal matrix in essence. The proposed matrix can be used to generate higher-order Euler-Jacket matrices efficiently and hence other similar real orthogonal matrices with fast algorithm. The proposed matrix is much more concision and frank than direct-computation which means Euler-Jacket transform is an efficient algorithm. Euler-Jacket transform is proved to have stability and simplicity in digital image processing simulation.