Data decorrelation by wavelet transform

The Wavelet Transform is not optimal for image compression. The coefficients on the same level of decomposition preserve a residual correlation which may harm the efficiency of the encoding algorithm. In the case of entropic codes, this effect can be reduced by using an appropriate coefficients scanning and long enough contexts for the conditional probabilities. Such an approach needs the knowledge of the residual correlation. This paper proposes a set of formulas for the evaluation of the coefficients correlation, based on the image and wavelet auto-correlations. The wavelet type and its length is shown to be unimportant for data decorrelation as proven by similar results on various cases. According to the proposed formulas, in the case of images with separable autocorrelation, the transformation of a coordinate preserves the other coordinate correlation. For classes of signals like images, with autocorrelation matching mathematical models, general encoding procedures could be provided based on these conclusions.