Compression of generalised Gaussian sources

Summary form only given. This article introduces a non-linear statistical approach to the interframe video coding assuming a priori that the source is non-Gaussian. To this end generalised Gaussian (GG) modelling and high-order statistics are used and a new optimal coding problem is identified as a simultaneous diagonalisation of 2nd and 4th order cumulant tensors. This problem, named the high-order Karhunen-Loeve transform (HOKLT), is an independent component analysis (ICA) method. Using the available linear techniques for cumulant tensor diagonalisation the HOKLT problem cannot be, in general, solved exactly. Considering the impossibility of solving HOKLT problem within the linear group, a non-linear methodology named non-linear independent components analysis (NLICA) that solves the HOKLT problem was introduced. The structure of the analysis operator produced by NLICA is a linear-nonlinear-linear transformation where the first linear stage is an isoentropic ICA operator and the last linear stage is a principal components analysis (PCA) operator. The non-linear stage is diagonal and it converts marginal densities to Gaussianity conserving marginal entropies. Considering the three basic coding modes within DPCM video coders and the three colour components there are nine different sources. Fitting this sources to GG family, done in this work, has shown how far from Gaussianity these sources are and supports the GG modelling effectiveness.