  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.
