CLASSIFIED SCALER ENTROPY CODING FOR INFORMATION-SOURCES WITH ELLIPTICALLY SYMMETRICAL PROBABILITY-DISTRIBUTION

When the subband transform coefficients of natural images at the same location are considered a vector, the vector often has an elliptically symmetric distribution where the probabilities are identical on an el liptic surface. This paper treats the coding loss of the scalar entrop y coding of a vector information source with an elliptically symmetric distribution. The multidimensional uncorrelated Gaussian distribution has the characteristics that no coding loss occurs even if the compon ents are independently coded, and that the information becomes concent rated in the elliptic shell as the number of dimensions increases. In this paper, we show that the one-dimensional marginal distribution of the multidimensional distribution concentrating in the elliptical shel l asymptotically approaches a Gaussian distribution. The classified sc alar entropy coding (CSEC) makes use of this fact; we first classify t he vector by its normalized norm, entropy-code, the classification ind ex, and each vector component. Next, under the assumption that the ell iptically symmetric distribution varies more slowly than the thickness of the Gaussian distribution shell, the coding loss of the CSEC metho d is derived. We show that the coding loss per dimension asymptoticall y approaches zero as the number of dimensions increases. Finally , the amount of information of the CSEC method is computed when the amplitu de distribution of the subband transform coefficients is modeled by th e generalized Gaussian distribution. The result is superior to the unc lassified scalar entropy coding method by 0.25 to 0.5 [bits/dim]. (C) 1998 Scripta Technica.