A Gamma Mixture Model for the Energy of Blocks Dedicated to Vector Quantization of Sparse Signals

Most of works related to vector quantization with structured codebooks deal with i.i.d. signal assumptions. We have shown in previous works that this hypothesis limited the efficiency of such coders applied on real signals. Indeed, we have proposed the use of a vector dead zone (VDZ) which outperforms previous schemes. The VDZ takes advantage of sparsity and clustering properties of sources like discrete wavelet transform of images. Here we give an interpretation of these properties under the angle of the norm distribution. We propose a probabilistic model of the norm of source sample blocks based on Gamma mixtures. Theoretical arguments, as well as experimental results show that our model fits well the source block distribution.