Optimal bi-level quantization and its application to multilevel quantization

A special form of optimal quantization, optimal bilevel quantization, is studied. A fixed-point method is embedded in a search scheme to find all the locally optimal bilevel quantizers, resulting in an algorithm for computing the globally optimal bilevel quantizer. Some interesting relations between the optimal bilevel quantizer, and the mean and the median of the density function p(x) are explored. Efficient algorithms for computing optimal bilevel quantizers are proposed. The application of these results to optimal quantization in general is discussed.<>