A 4D nth-order Walsh orthogonal transform algorithm used for color image coding

Abstract

Based on the multi-dimensional matrix theory, this paper introduced four-dimensional (4D) model, and deduce the Walsh orthogonal transform in 4D nth-order matrix space. This method is used for color image coding. We obtained very good results. 4D nth-order matrix model can express 4D data in a unified mathematical model for processing. On one hand, it considers the high efficiency of classical matrix transform in the aspect of removing redundancy of color space. On the other hand, it overcomes the restriction of traditional two-dimensional matrix multiplication. Favorable image compression effect can be obtained by 4D Walsh orthogonal transform and traditional discrete cosine transform.