Optimal entropy constrained scalar quantization for exponential and Laplacian random variables

This paper presents solutions to the entropy-constrained scalar quantizer (ECSQ) design problem for two sources commonly encountered in image and speech compression applications: sources having exponential and Laplacian probability density functions. We obtain the optimal ECSQ either with or without an additional constraint on the number of levels in the quantizer. In contrast to prior methods, which require iterative solution of a large number of nonlinear equations, the new method needs only a single sequence of solutions to one-dimensional nonlinear equations (in some Laplacian cases, one additional two-dimensional solution is needed). As a result, the new method is orders of magnitude faster than prior ones. We also show that as the constraint on the number of levels in the quantizer is relaxed, the optimal ECSQ becomes a uniform threshold quantizer (UTQ) for exponential, but not for Laplacian sources