Robust Quantization of ε-Contaminated Data

Abstract

The problem of robust quantization of data with uncertain statistical properties is considered. Uncertainty in the statistics of the data is modeled by assuming that the data have a probability density function of the ε-contaminated form, and a minimax approach to robust design is adopted. An approximation is developed for the asymptotic worst-case distortion (over the ε-contaminated class) produced by an arbitrary companded quantizer, and the quantizer design which minimizes this worst-case distortion is derived. The robustness of the resulting design is verified numerically for the particular problem of quantizing ε-contaminated Gaussian data.