A minimum-risk quantizer for noisy sources

The problem of quantizing noisy signals in an optimal manner is addressed. Quantizer designs relying on training sets, "clean" probability statistics, or composite statistics of source and noise, will yield designs which are sub-optimal and possibly detrimental to system performance. The concept of the quantizer as an estimator is used in conjunction with a risk function to produce a minimum risk quantizer for noisy sources. In particular, the minimum-risk quantizer design theory for the case of independent, identically distributed source with additive (i.i.d.) noise is developed. The minimum-risk quantizer criteria for the specific problem of a source signal with gaussian statistics corrupted by additive gaussian noise and the squared-error cost function is produced. It is further shown that the Max-Lloyd optimal quantizer criteria is a subset of the minimum-risk criteria for noiseless conditions.