Scalar quantization noise analysis and optimal bit allocation for a wavelet pyramid image coding system

A complete analysis for the reconstruction noise due to the scalar quantization of a wavelet pyramid image coding system is given. It is shown that when the optimal bit allocation scheme is adopted, the reconstruction noises and the quantization noises of the wavelet pyramid system become regular, and that the reconstruction noises can be approximated to stationary white noises. Particularly, it is shown that with only one quantization mean-square-error (MSE) of the wavelet decomposition at any layer of the wavelet pyramid, all of the reconstruction MSEs and the quantization MSEs of the wavelet pyramid can be easily calculated. Simulations verify the theoretical results