Quantization Dimension Function and Ergodic Measure with Bounded Distortion

The Canonical Distortion Measure for Vector Quantization and Function Approximation

To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an environment of functions on an input space X induc...

Quantization with an Information-Theoretic Distortion Measure

Boosting quantization for Lp norm distortion measure

Quantization is a widely used technique in signal processing. The purpose of many quantization schemes is to faithfully reproduce the input signals. However, in many situations, one is more interested in comparison of different classes of signals in order to classify them into different categories. The classification criterion is based on comparing distances under certain metric. For classical ...

Quantization Dimension for Conformal Iterated Function Systems

Quantization with Lagrangian Distortion Measures

The Lagrangian formulations of fixedrate and variable-rate vector quantization can be combined into a single formulation involving constraints on both entropy and log codebook size. The approach leads to a Lloyd design algorithm and to results on high-rate or high-resolution quantization. It provides both a unified view of the traditional results and an approach to studying the implications of ...