The high resolution vector quantization problem with Orlicz norm distortion

TitleThe high resolution vector quantization problem with Orlicz norm distortion
Publication TypeJournal Article
Year of Publication2010
AuthorsSteffen Dereich, and Christian Vormoor
Keywordscomplexity, discrete approximation, High-resolution quantization, self similarity
Abstract

Summary. We derive a high-resolution formula for the quantization problem under Orlicz norm distortion. In this setting, the optimal point density solves a variational problem which comprises a function  \mathbb{R_+} \to [0,\infty) $ characterizing the quantization complexity of the underlying Orlicz space. Moreover, asymptotically optimal codebooks induce a tight sequence of empirical measures. The set of possible accumulation points is characterized and in most cases it consists of a single element. In that case, we find convergence as in the classical setting.