An analytical Gamma mixture based Rate-Distortion model for lattice vector quantization

Here we propose a new blockwise Rate-Distortion (R-D) model dedicated to lattice vector quantization (LVQ) of sparse and structured signals. We first show that the clustering properties leads to a distribution of the norm L^α of source vectors close to a mixture of Gamma density. From this issue, we derive the joint distribution of vectors as a mixture of multidimensional generalized gaussian densities. This data modelling not only allows us to compute more accurate analytical R-D model for LVQ but provides a new theoretical framework to the design of codebooks better suited to data like dead zone LVQ [5, 12].