Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video

Abstract

A subband decomposition scheme for video signals, in which the original or difference frames are each decomposed into 16 equal-size frequency subbands, is considered. Westerink et al. [4] have shown that the distribution of the sample values in each subband can be modeled with a "generalized Gaussian" probability density function (pdf) where three parameters, mean, variance, and shape are required to uniquely determine the pdf. To estimate the shape parameter, a series of statistical goodness-of-fit tests such as Kolmogorov-Smirnov or chi-squared tests have been used in [4]. A simple alternative method to estimate the shape parameter for the gencralizcd Gaussian pdf is proposed that significantly reduces the number of computations by eliminating the need for any statistical goodness-of-fit test. ~NTRODr'('7'10NSubband decomposition is used in video and image processing a\ a compression tool. The signal is decomposed into frequency wbbands and each subband is encoded independently. In ii lossy encoding scheme. the sample values in each subband. or their prediction errors after passing through a DPCM loop. are quantized. To design an appropriate quantizer, the distribution of the subband samples needs to be known [ I ] . It has been assumed that the probability density function of the subband values and their prediction errors is Lnp/uc,iarz [2], 131. While this assumption seems more valid for the prediction errors of the sample values. the Laplacian distribution cannot adequately model the distribution of sample values.Figs. 1 and 2 show the histograms of two subbands generated from the Flower sequence. The histogram of subband 2 of the original frame 1 and the histogram of subband 2 of the difference between frame 1 and frame 2 along with the Laplacian pdf's with the same mean and variance are shown, respectively. The mismatch between the test Laplacian pdf's and the actual histograms has also been observed for other test sequences.Westerink rf ci/. 141 have shown that the distribution of' the sample values in each subband can be modeled with a generalized Gaussian pdf where three parameters. namely. mean. variance. and shape. are required to uniquely specify the analytic pdf. In this paper. we propose :I simple method that enables us to tind the best shape parameter for the generalired Gaussian distribution that best tits the data of each subband.In Section II. the class of generalized Gausian pdf's as the best candidate for this purpose is presented. To determine the best shape parameter for generalized Gaussian pdf, a simple method is developed in Section 111. Section IV contains the simulation results and concluding remarks are presented in Section V. G~NERALIZED GALWAN PDFThe class of genrrrr1i:rd Gcrus.sitrri probability distribution functions has been used in 141 to model the distribution of the subband values of images. It has been shown that this class of pdYs can

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