Name
Abstract | ||
|---|---|---|
We consider the problem of optimal randomized vector quantization under a constraint on the output's distribution. The problem is formalized by introducing a general representation of randomized quantization via probability measures over the space of joint distributions on the source and reproduction alphabets. Using this representation and results from optimal transport theory, we show the existence of an optimal (minimum distortion) randomized quantizer having a fixed output distribution under various conditions. For sources with densities and the mean square distortion measure, we show that this optimum can be attained by randomizing quantizers having convex code cells. We also consider a relaxed version of the problem where the output marginal must belong to some neighborhood (in the weak topology) of a fixed probability measure. We demonstrate that finitely randomized quantizers form an optimal class for the relaxed problem. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/ISIT.2013.6620646 | ISIT |
Keywords | Field | DocType |
distortion,optimisation,probability,quantisation (signal),convex code cells,fixed output distribution,fixed probability measure,joint distributions,marginal constraint,mean square distortion measure,minimum distortion randomized quantizer,optimal class,optimal design,optimal randomized quantizer,optimal randomized vector quantization,optimal transport theory,probability measures,relaxed problem,reproduction alphabets,source alphabets,weak topology | Discrete mathematics,Mathematical optimization,Combinatorics,Weak topology,Joint probability distribution,Probability measure,Regular polygon,Optimal design,Vector quantization,Quantization (signal processing),Distortion,Mathematics | Conference |
Citations | PageRank | References |
5 | 0.44 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Naci Saldi | 1 | 29 | 10.27 |
| Tamás Linder | 2 | 617 | 68.20 |
| Serdar Yüksel | 3 | 457 | 53.31 |