PYRAMID TRANSFORM CODING

In the pyramid transform coding, the input image of size 2n x 2n is first decomposed into a set of blocks of size 2m x 2m, where m < n. Then, each block undergoes a two-dimensional discrete cosine transform 2D-DCT of size 2m x 2m. The resulting coefficients are reorganised into 2m x 2m transform subimages of size 2n-m x 2n-m, each corresponding to a coefficient order. For each subimage, a transform mean subpyramid is formed by successively averaging over 2 x 2 neighbouring values. The corresponding transform difference subpyramid is then built up by taking the differences between successive levels in the transform mean subpyramid. The 2m x 2m transform difference subpyramids are concatenated and rearranged to form a transform difference pyramid. The transform difference pyramid can be used to form a transform mean pyramid, where the intermediate levels of the transform mean pyramid are simply the reduced-size approximations of the block transformed image. This implies that progressive image transmission can be achieved by transmitting the transform difference pyramid. The transform difference pyramid is shown to reduce the correlation between the neighbouring transform blocks. Therefore, more efficient transmission is obtained by transmitting the transform difference pyramid, instead of the original block DCT image and the transform mean pyramid. Before transmission, the transform difference pyramid is either scale or vector quantised and encoded starting from the top level where the residual errors introduced at each level are delivered to and reprocessed at the next level. The simulation results demonstrate that, by using vector quantisation, excellent quality is achieved at a bit rate of about 0.55 bits/pixel. The pyramid transform coding scheme is shown to be competitive with variable-length transform coding,