Optimal reconstruction from quantized data

摘要

Data quantization is an essential step before digitization, i.e. prior to representing real numbers by bits for further digital processing. In this paper we show how a statistically non-optimal quantizer (e.g. a uniform quantizer) can be improved by a simple scaling operation before reconstructing the original value. The scale factor depends on the statistics of the input and it is not constant, except for the case of the optimal Lloyd–Max quantizer where it is always equal to 1. However in other cases, for example in the common uniform quantizer we report improvement of the order of 0.1–0.6 db depending on the bit-rate. The proposed method can be used in any application where uniform (or other non-optimal) quantizers are used. In particular, it can be used for the quantization scheme of the JPEG image coding standard, and elsewhere.