ANTONINI ef al. IMAGE CODING USING WAVELET TRANSFORM Real PDF. legalized r=0.7) Laplace Wavelet coefficients Fig. 9. Real PDF of subimage at scale m a I for vertical orientation. and its different approximations. CODER index 2)Comparative Performances of vector quantization (vQ) and Scalar Quantization ( ccording to I [13]. [191, [43], [30] the asymptotic lower bound distor tion gain obtained when VQ, rather than SQ, is applied 之 (c I)A(k,md, c) Lpm.dx) J Ipm ()-/c +im a dr Fig. 11, Asymptotic lower bound distortion gain Gw,= function (km., and generalized Gaussian approximation laws, and for a for a subimage corresponding to resolution m and direc- subimage at scale m 1 and vertical orientation. Exper tion d. Pm, d(x) is the PDF of wavelet coefficients of the imental results are closely matched by the theoretical re- subimage with resolution m and direction d sults for a generalized Ga ian law with md=0.7 Here, the MSE criterion is used as a distortion measure cept for the lower subband. Therefore, all computations (c-2). The values of A(km. d, 2)used are the upper based on this approximation law show that, in each sub bounds of the MSE computed and tabulated by Conway band, VQ outperforms SQ(see Fig. 11) and Sloane for vector size km, d [13]. This formula gives In summary vQ performs better for coding wavelet an indication of the minimum theoretical gain that can be coefficients 3)Generation of a Multiresolution Codebook: The However, this approximation is valid only for small preceding paragraph explained why Q outperforms other quantization erro for a high bit rate Rm,, d. Thus the methods. Nonetheless, major problems are encountered an as mitotic indication in the vQ of images In Fig. 11, the of G m d are plotted as a function It is impossible to create a universal codebook(effi of the vector dimension km, d for the Laplacian, Gaussian, cient for each image to be encoded)