Accurate rate-distortion approximation for sparse Bernoulli-Generalized Gaussian models

The objective of this paper is to study rate-distortion properties of a quantized Bernoulli-Generalized Gaussian source. Such source model has been found to be well-adapted for signals having a sparse representation in a transformed domain. We provide here accurate approximations of the entropy and the distortion functions evaluated through a p-th order error measure. These theoretical results are then validated experimentally. Finally, the benefit that can be drawn from the proposed approximations in bit allocation problems is illustrated for a wavelet-based compression scheme.