Noisy Source Vector Quantization Using Kernel Regression

The problem of designing an optimal vector quantizer when there is access to the noise-free source has been well studied over the past five decades. However, in many real-world situations, the source output may be corrupted by some additive noise. In this case, we only have access to a noisy version of the data, but we expect a designed quantizer to minimize the distortion with respect to the clean (unavailable) data. It can be shown that the mean square distortion for an optimal noisy source vector quantization system can be decomposed into an optimum estimator, followed by an optimum source coder operating on the estimator output. We summarize this result first and then propose to use the kernel regression technique for estimating the clean data from the noisy version. The output of the kernel regression, as an estimate of the clean data, is quantized using the LBG vector quantizer. The proposed structure requires two sets of training data. The first set is used to train the kernel regression estimator. The second set is fed into the trained kernel regression system whose output is used to train the LBG vector quantizer. We show the effectiveness of the proposed structure through simulations with different numbers of code words.