On Distribution Preserving Quantization

Upon compressing perceptually relevant signals, conventional quantization generally results in unnatural outcomes at low rates. We propose distribution preserving quantization (DPQ) to solve this problem. DPQ is a new quantization concept that confines the probability space of the reconstruction to be identical to that of the source. A distinctive feature of DPQ is that it facilitates a seamless transition between signal synthesis and quantization. A theoretical analysis of DPQ leads to a distribution preserving rate-distortion function (DP-RDF), which serves as a lower bound on the rate of any DPQ scheme, under a constraint on distortion. In general situations, the DP-RDF approaches the classic rate-distortion function for the same source and distortion measure, in the limit of an increasing rate. A practical DPQ scheme based on a multivariate transformation is also proposed. This scheme asymptotically achieves the DP-RDF for i.i.d. Gaussian sources and the mean squared error.