SCALAR QUANTIZATION NOISE-ANALYSIS AND OPTIMAL BIT ALLOCATION FOR WAVELET PYRAMID IMAGE-CODING

A complete analysis for the quantization noises and the reconstruction noises of the wavelet pyramid coding system is given. It is shown that in the (orthonormal) wavelet image coding system, there exists a simple and exact formula to compute the reconstruction mean-square-error (MSE) for any kind of quantization errors. Based on the noise analysis, an optimal bit allocation scheme which minimizes the system reconstruction distortion at a given rate is developed. The reconstruction distortion of a wavelet pyramid system is proved to be directly proportional to 2(-2 RBAR), where RBAR is a given bit rate. It is shown that, when the optimal bit allocation scheme is adopted, the reconstruction noises can be approximated to white noises. Particularly, it is shown that with only one known quantization MSE of a wavelet decomposition at any layer of the wavelet pyramid, all of the reconstruction MSE's and the quantization MSE's of the coding system can be easily calculated. When uniform quantizers are used, it is shown that at two successive layers of the wavelet pyramid, the optimal quantization step size is a half of its predecessor, which coincides with the resolution version of the wavelet pyramid decomposition. A comparison between wavelet-based image coding and some well-known traditional image coding methods is made by simulations, and the reasons why the wavelet-based image coding is superior to the traditional image coding are explained.