基于多维矢量矩阵正交变换理论的彩色图像压缩编码

Color image coding based on multidimensional vector matrix discrete cosine transform theory

在多维矢量矩阵理论的基础上提出了四维矢量矩阵离散余弦变换(4D-VMDCT)算子,扩展了多维矢量矩阵正交变换理论,验证了该变换算子的正交性和能量集中性;提出了适应于三维数据的量化方法,并将该方法用于图像压缩。根据彩色图像的行、列、颜色分量之间的强相关性构建了多维矢量矩阵采样模型,进行多维正交变换,大幅降低了多维数据的相关性,并通过多维量化和无损熵编码,进一步消除统计冗余。理论分析和实验结果表明:在增加压缩比的同时,峰值信噪比也有明显的提高,实验结果优于国际标准JPEG。

The theory of multidimensional vector orthogonal transformation matrix was extended.A new 4-D vector matrix Discrete Cosine Transform（DCT） operator was presented based on the theory.In addition,the orthogonality of the operator and energy concentration were verified.Also a technique was proposed to generate the quantization cube suitable to Multidimensional Vector Matrix DCT（MD-VMDCT） transform codec.A sampling model for 3D Vector Matrix DCT（3D-VMDCT） codec was also proposed,which can eliminate spatial redundancy and color redundancy among the pixels in the color image by use of the supper concentration of the MD-VMDCT.Then quantization and Huffman coding were carried out to eliminate statistical redundancy.Experimental results show that the algorithm is correct and effective,and under the same conditions it outperforms the Joint Photographic Experts Group（JPEG） method.