Quantization Based on the Mean-Absolute-Error Criterion

Performance criteria for the design of optimum quantizers are considered. A distance criterion for quantizer input and output probability distribution functions is formulated, and its relationship to the usual distortion criteria is established. The criterion based on absolute error is shown to have unique properties, justifying its use as a performance index for optimum quantization. Numerical results are presented, and the implication for adaptive quantization of the use of this criterion is discussed.