Some Remarks on Optimal Quantization.
Efren F. Abaya, G.L. Wise · Defense Technical Information Center (DTIC) · 1982
Current numerical algorithms for constructing optimal quantizers encounter difficulties if either an optimal solution does not exist, or if local minima are present. In this paper, the authors show that an optimal quantizer may not always exist, and present a condition on the distortion measure and another condition on the probability distribution, either of which guarantees existence of an optimal solution. Then, we comment on the role of symmetry in optimal quantization and discuss the validity of one method that has been used to prove uniqueness of the optimal solution.