Scalar quantisation of heavy-tailed signals

Efficient stochastic data processing presupposes proper modelling of the statistics of the data source. The authors address the issues that arise when the data to be processed exhibits statistical properties which depart significantly from those implied under the Gaussianity assumption. First, they present a study on the modelling of coefficient data obtained when applying the wavelet transform (WT) to images. They show that WT coefficients are heavy-tailed and can be modelled with alpha-stable distributions. Then, they introduce an alternative to the common mean-square error (MSE) quantiser for the efficient, scalar quantisation of heavy-tailed data by means of distortion minimisation. The proposed quantiser is based on a particular member of the family of alpha-stable distributions, namely the Cauchy distribution, and it employs a distortion measure based on the mean square root absolute value of the quantisation error. Results of the performance of this quantiser when applied to simulated as well as real data are also presented