Laplacian pyramid encoding: optimum rate and distortion allocations

The authors develop the optimum bit allocations for fixed rate (minimum distortion) and fixed distortion (minimum rate) hierarchical Laplacian pyramid image coding structures, using scalar quantizers that have negative exponential quantizer functions. The optimum MSE (mean square error) bit allocation is shown to agree closely with P.J. Burt and E.H. Adelson´s (IEEE Trans. Acoust., Speech and Signal Proc., vol. ASSP-34, p.1278-88, Oct. 1987) empirically derived and perceptually based allocation. The slope of the distortion-rate function is found to vary with the number of levels, N, in the pyramid, becoming worse as N increases. It is also shown that since the amount of compression is a function of the distribution of energies among the Laplacian images, performance is strongly affected by the quality of the filters. The analysis permits comparison with other important schemes, such as subband coding, from a distortion-rate perspective