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 quantizers, although the individual quantized signal may show high fidelity to its original signals, the distance features characterizing different categories may not be well reserved, which results in poor performance of classification in spite of relatively good reproduction of individual signals. In this paper, we propose a special optimal quantization under the Lp norm distortion measure called Boosting Quantization. The quantization is guaranteed to preserve the distances of different classes. We provide a quantization algorithm to generate the quantizer. We also derive several theoretical properties for the proposed quantization. Finally, we provide numerical examples to illustrate our proposed boosting quantization.