Random Quantization: A New Analysis with Applications

The study of quantization in undoubtedly of extreme importance to all fields relying on a digital representation of the information, such as the fields of Signal and Image processing. This paper presents a new general framework of random quantization theory which encompasses the entire classes of deterministic (i.e. non-dithered) and dithered quantizers. Two new statistical characterizations of a random quantizer (RQ) are given in the form of 2 new alternative expressions of the RQ’s p-order moment-sense input/output function , one of which is used to explain the unique smoothing property of RQs. A general expression relating any finite-order moment of the RQ’s output and its MSIOF is derived. Finally, some representative results of a successful application of a special type of 1-bit RQ to exact moment recovery are shown, and other applications discussed. ) (x hp