An Optimally Bit Allocated Wavelet Pyramid Image Coding System

Reconstruction error properties for a wavelet pyramid image coding system are described. It is shown that when optimal bit allocation scheme is adopted, the reconstruction noises and the quantization noises of the wavelet pyramid coding system become regular, and the reconstruction noises can be approximated to stationary white noises. Based on the error property analysis, an optimal bit allocation scheme with respect to the minimum reconstruction-mean-square-error (RMSE) criterion is given. The system reconstruction distortion at a given bit rate R is proved to be directly proportional to 2-2R. Experimental results are given. Summary a J-stage discrete orthonormal wavelet pyramid image coding system [2], kt {PJ, (D;)I~~~J, (D;)I<,<J, (~~)I~~~J} be the wavelet decompositions of an input image Po and let {EJ, (E:)IC~~J, (E;)I~~<J, (E;)IC~<J} be their quantization MSE’s, respectively. Furthermore, let cj denote the reconstruction MSE at 9-th layer of the pyramid. Based on the orthonormality of the discrete orthonormal wavelets and signal processing theory, the reconstruction MSE at a layer is given as J3 Ej-1 = Ej+xxE!,