On the coding gain of wavelet transforms

The coding gain of biorthogonal wavelet transforms is investigated. The influence of the regularity and number of vanishing moments of these wavelets on the coding gain is analysed. More than 80 wavelet transforms are assessed. The results show that as long as the coding gain of a wavelet transform is reasonably high, the influence of both regularity and number of vanishing moments on the coding gain is low. On the other hand, for wavelet transforms with coding gains less than 1, the coding gain decreases when the regularity decreases. It is also shown that, in some cases, the coding gain of biorthogonal wavelet transforms is larger than the theoretical maximum for orthogonal transforms, obtained with ideal filters. In addition, unlike orthogonal transforms, whose coding gain in octave decompositions is always smaller than the one obtained with uniform band decompositions with the same number of stages and filter banks, the coding gain of biorthogonal transforms in octave band decompositions can be either larger or smaller than in the uniform case