Quantizer monotonicities and globally optimal scalar quantizer design

摘要

New monotonicity properties of optimal scalar quantizers are discussed. These monotonicities reveal a globally optimal scalar quantizer structure depending on the probability mass functions and on the number of quantizer levels. By incorporating the monotone quantizer structure into a dynamic programming process, the time complexities of previous algorithms for designing globally optimal scalar quantizers can be significantly reduced for very general classes of distortion measures.