离散余弦变换对图象信号有近似最优的去相关能力，但多维的变换公式一直没有给出，为此深入研究了三维离散余弦变换，提出了任意尺寸的三维函数f(x,y,z)的正交离散余弦变换公式，克服了以前系数的取值必须相等的缺点，并将之应用于彩色静止图象的压缩编码中，使得彩色图象的R，G，B3帧可以作为一个整体同时进行变换，极大地去除了图象R，G，B3帧间的相关性，理论分析和实验结果表明，在大幅度地增加压缩比的同时，峰峰信噪比也有明显提高，并且与国际标准JPEG，MPEG有很好的兼容性。

Discrete Cosine Transform(DCT) can decrease the relativity among the images, but we didn't know the muldimension DCT accurately. In this paper, three dimensional Discrete Cosine Transform(DCT) has been researched, its calculate method, transform and inverse transform were given, and any sizes of three dimensional function f(x,y,z) DCT is proposed, that must be cube before. As we known, it is identity physics model unify reflection into that of color image's three frame, possess same texture, same fringe and same gray change, the information of the each frame almost could reflect the source image except color, the vision similitude are very strong. In other methods, R, G, B data were transformed into Y, Cr, and Cb to decrease the color information. It is clear that if we encode Y Cr Cb data separately, among each component potential relativity can't be decreased enough. So we regard R, G, and B as a whole, transform them in the same time with three dimensional DCT. It can decrease relativity between frames than before. Simulation results demonstrate good reconstruction image quality and high compression ratio. It has good compatible with JPEG and MPEG standard.