Are the Wavelet Transforms the Best Filter Banks for Image Compression?

Maximum regular wavelet filter banks have received much attention in the literature, and it is a general conception that they enjoy some type of optimality for image coding purposes. To investigate this claim, this article focuses on one particular biorthogonal wavelet filter bank, namely, the 2-channel 9/7. As a comparison, we generate all possible 9/7 filter banks with perfect reconstruction and linear phase while having a different number of zeros at z=−1 for both analysis and synthesis lowpass filters. The best performance is obtained when the filter bank has 2/2 zeros at z=−1 for the analysis and synthesis lowpass filters, respectively. The competing wavelet 9/7 filter bank, which has 4/4 zeros at z=−1, is thus judged inferior both in terms of objective error measurements and informal visual inspections. It is further shown that the 9/7 wavelet filter bank can be obtained using gain-optimized 9/7 filter bank.