New fast algorithm for hypercomplex decomposition and hypercomplex cross-correlation

In order to calculate the cross-correlation of two color images treated as vector in a holistic manner, a rapid vertical/parallel decomposition algorithm for quaternion is  resented. The calculation for decomposition is reduced from 21 times to 4 times real number multiplications with the same results. An algorithm for cross-correlation of color images based on decomposition in time domain is put forward, in which some properties pointed out in this paper can be utilized to reduce the computational complexity. Simulation results show the effectiveness and superiority of the proposed method.