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. Index Terms Distribution preserving quantization, Rate-distortion function, Shannon lower bound. M. Li, and J. Klejsa are with the School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden. e-mail: {minyue.li, janusz.klejsa}@ee.kth.se W. B. Kleijn is both with the School of Engineering and Computer Science, Victoria University of Wellington, Wellington, New Zealand and with the School of Electrical Engineering, KTH Royal Institute of Technology, Stockholm, Sweden. email: [email protected]