Title :
On Codecell Convexity of Optimal Multiresolution Scalar Quantizers for Continuous Sources
Author_Institution :
Comput. & Autom. Res. Inst., Budapest, Hungary
Abstract :
It has been shown by earlier results that for fixed rate multiresolution scalar quantizers and for mean squared error distortion measure, codecell convexity precludes optimality for certain discrete sources. However it was unknown whether the same phenomenon can occur for any continuous source. In this paper, examples of continuous sources (even with bounded continuous densities) are presented for which optimal fixed rate multiresolution scalar quantizers cannot have only convex codecells, proving that codecell convexity precludes optimality also for such regular sources.
Keywords :
mean square error methods; quantisation (signal); codecell convexity; continuous sources; fixed rate multiresolution scalar quantizers; mean squared error distortion measures; optimal multiresolution scalar quantizers; Algorithm design and analysis; Approximation methods; Atomic measurements; Entropy; Probability density function; Source coding; Technological innovation; Clustering methods; codecell convexity; continuous density function; mean squared error methods; multiresolution; optimization methods; quantization; rate distortion theory; source coding;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2173708
