Multi-dimensional vector matrix theory and its application in colour image coding

Abstract

Based on matrix theory, the concept of two-dimensional matrix is extended to fit multi-dimensional matrix. In order to reduce the space redundancy, time redundancy and colour redundancy better, we propose a multi-dimensional vector matrix model. Some related properties are discussed, and Walsh orthogonal square matrix is given in multi-dimensional vector matrix space, then its application in colour image compression and coding is introduced. By means of multi-dimensional vector matrix model, colour image data can be expressed and processed in a unified mathematical model, and better compression results are obtained. On the one hand, it inherits high efficiency of classical matrix transform in the aspect of wiping off redundancy of colour space; on the other hand, it overcomes the restriction of traditional two-dimensional matrix multiplication. By multi-dimensional Walsh orthogonal transform and traditional discrete cosine transform, favourable image compression effect can be obtained.