The scale-based pyramid weighting of the wavelet coefficients in zerotree coding techniques

The efficiency of all zerotree coding algorithms relay on the "decaying spectrum" hypothesis: a wavelet coefficient within a certain frequency scale of a wavelet subband decomposition has a larger magnitude than all his descendants (coefficients situated in higher frequency scales having the same spatial orientation). The higher the percentage this hypothesis is satisfied, the better are the results delivered by the zerotree algorithms (in terms of PSNR and bitrate). The paper proposes a technique enforcing this hypothesis to be satisfied: scale-based pyramid weighting of the wavelet coefficients. Each scale of coefficients will be amplified with respect of the next higher frequency scale so that lower frequency scales (from the top of the wavelet decomposition pyramid) will have a higher amplification than lower frequency scales (from the base of the pyramid). There are also presented two equivalent techniques: scale-based reverse-pyramid weighting of the thresholds, and the use of supra-unitary norm wavelet filters in subband decomposition step.