Data Compression: The Complete Reference

5.10 Various Image Decompositions 579frequency representation of the image), with the rest of the image giving rise to a fewlarge subbands. The bottom-left coefficient matrix in Figure 5.46 is an example of avery uniform image, resulting in just 10 subbands. (The test for a split depends on theabsolute magnitude of the transform coefficients. Thus, the test can be adjusted so highthat very few splits are done.)Temporary LOriginalimageTemporary HLLLHHLHHTemporary LTemporary HTemporary LTemporary HLLLL LLLH LLHL LLHHHLLL HLLH HLHL HLHHLLLLLLHLHLLLHLHLLLLHLLHHHLLHHLHHLHHHFigure 5.46: Adaptive Wavelet Packet Decomposition.The main problem in this type of decomposition is finding an algorithm that willdetermine which subband splits can be skipped. Such an algorithm uses entropy calculationsand should be efficient. It should identify all the splits that do not have to beperformed, and it should identify as many of them as possible. An inefficient algorithmmay lead to the split of every subband, thereby performing many unnecessary computationsand ending up with a coefficient matrix where every coefficient is a subband, inwhich case this decomposition reduces to the uniform decomposition.This type of decomposition has the highest reproduction quality of all the methodsdiscussed here, a feature that may justify the high computational costs in certain special