Scalar Quantization of Alpha Stable Distributed Random Variables

E cient stochastic data processing preassumes proper modeling of the statistics of the data source This paper addresses the issues that arise when the data to be pro cessed exhibits statistical properties which depart signi cantly from those implied under the Gaussianity assump tion This type of data has been found to be encountered in image speech and other compression applications For the cases under consideration techniques based on the sta tistical theory of alpha stable distributions have been found to give the most proper solution to the modeling problem Furthermore an alternative to the common mean square error MSE quantizer for the e cient by means of distor tion minimization scalar quantization of heavy tailed data is presented The proposed quantizer is based on a par ticular member of the family of alpha stable distributions namely the Cauchy distribution The results of the perfor mance of this quantizer when applied to simulated as well as real data are also presented