Redundancy-Driven A Posteriori Matching Pursuit Quantization

This paper studies quantization error in the context of Matching Pursuit coded streams. The quantization noise is shown to depend on error on both coefficients and indexes. It is moreover influenced by the redundancy of the Matching Pursuit dictionary. A novel general formulation of the structural redundancy in overcomplete decompositions is shown to enhance the accuracy of classical redundancy factors. The redundancy factor drives the decay of Matching Pursuit coefficients energy and is therefore used to design an optimal a posteriori quantization scheme for multi-resolution Matching Pursuit coding. This exponentially upper-bounded quantization of Matching Pursuit coefficients clearly outperforms uniform quantization schemes in the practical case of image coding. The atom selection error is then studied for structured dictionaries and more particularly dictionaries built upon common Gabor functions. This analysis is used to quantify the error in the case of a simple scalar quantization of structured atom indexes. Finally, it is shown that a posteriori scalar indexes quantization should be preferably avoided, thus emphasizing the need for a careful dictionary design as a trade-off between compression efficiency and code size.