Robust Quantization of ε-Contaminated Data

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.