On the structure of optimal entropy-constrained scalar quantizers
On the structure of optimal entropy-constrained scalar quantizers
复制标题
关于最优熵约束标量量化器的结构
DOI：
10.1109/18.978755
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
T. Linder
中科院分区：
文献类型：
--
作者：
A. György;T. Linder
最近邻条件意味着当搜索均方最佳固定速率量化器时，考虑常规量化器的类别就足够了，即具有凸单元和位于相关单元内部的码点的量化器。相反，量化器规律性可能会妨碍熵约束量化中的最优性。这可以通过展示一个简单的离散标量源看出，其中均方最优熵约束标量量化器 (ECSQ) 以一定的速率断开（因此非凸）单元。在这项工作中，提出了关于最优 ECSQ 的结构和存在的新结果。一个主要结果表明，对于 d(x,y)=/spl rho/(|x-y|) 形式的连续源和失真测量，其中 /spl rho/ 是非递减凸函数，任何有限级 ECSQ 都可以“正则化”，以便生成的正则量化器具有相同的熵和相等或更少的失真。关于最优 ECSQ 的存在性，我们证明在相当一般的条件下，对于任何熵约束都存在一个“几乎规则的”最优 ECSQ。对于平方误差失真测度和具有分段单调和连续密度的源，显示了常规最优 ECSQ 的存在性。
The nearest neighbor condition implies that when searching for a mean-square optimal fixed-rate quantizer it is enough to consider the class of regular quantizers, i.e., quantizers having convex cells and codepoints which lie inside the associated cells. In contrast, quantizer regularity can preclude optimality in entropy-constrained quantization. This can be seen by exhibiting a simple discrete scalar source for which the mean-square optimal entropy-constrained scalar quantizer (ECSQ) has disconnected (and hence nonconvex) cells at certain rates. In this work, new results concerning the structure and existence of optimal ECSQs are presented. One main result shows that for continuous sources and distortion measures of the form d(x,y)=/spl rho/(|x-y|), where /spl rho/ is a nondecreasing convex function, any finite-level ECSQ can be "regularized" so that the resulting regular quantizer has the same entropy and equal or less distortion. Regarding the existence of optimal ECSQs, we prove that under rather general conditions there exists an "almost regular" optimal ECSQ for any entropy constraint. For the squared error distortion measure and sources with piecewise-monotone and continuous densities, the existence of a regular optimal ECSQ is shown.