A Posteriori Quantized Matching Pursuit
This paper studies quantization error in the context of Matching Pursuit coded streams and proposes a new coefficient quantization scheme taking benefit of the Matching Pursuit properties. The coefficients energy in Matching Pursuit indeed decreases with the iteration number, and the decay rate can be upper-bounded with an exponential curve driven by the redundancy of the dictionary. The redundancy factor is therefore used to design an optimal a posteriori quantization scheme for multi-resolution Matching Pursuit coding. Bits are optimally distributed between successive coefficients according to their relative contribution to the signal representation. The quantization range and the number of quantization steps are therefore reduced along the iteration number. Moreover, the quantization scheme selects the optimal number of Matching Pursuit iterations to be coded to satisfy rate constraints. Finally, the new exponentially upper-bounded quantization of Matching Pursuit coefficients clearly outperforms classical uniform quantization methods for both random dictionaries and Gabor dictionaries in the practical case of image coding.