III Standards-Based Codecs (Continued...)

Generic Model

Spatial Redundancy Reduction Scheme (continued...)

Denote f(i,j) as original spatial-domain samples in the 8x8 block as show in Figure 6. and the resultant 8x8 block as F(u,v), then the DCT equation [1] is then:

(1) The size 8 x 8 is chosen due to its low memory requirement and computational complexity in most platforms. The reason DCT is mostly used is because of the benefits:

For highly correlated data, the compaction efficiency of DCT is close to that obtained with Karhunen-Loeve Transform but is easier to implement.
If the output of DCT, Y=TXT', where T' is the transpose matrix of T. Then the inverse transform is X=T'XT. So for a compression/decompression codec which require both forward and inverse transform, the orthogonality of the transform greatly reduces the complexity of the codec.