Metrics for vector quantization-based parametric speech enhancement and separation

Speech enhancement and separation algorithms sometimes employ a two-stage processing scheme, wherein the signal is first mapped to an intermediate low-dimensional parametric description after which the parameters are mapped to vectors in codebooks trained on, for example, individual noise-free sources using a vector quantizer. To obtain accurate parameters, one must employ a
good estimator in finding the parameters of the intermediate representation, like a maximum likelihood estimator. This leaves some unanswered questions, however, like what metrics to use in the subsequent vector quantization process and how to systematically derive them. This paper aims at answering these questions. Metrics for this are presented and derived, and their use is exemplified on a number of different signal models by deriving closed-form expressions. The metrics essentially take into account in the vector quantization process that some parameters may have been estimated more accurately than others and that there may be dependencies between the estimation errors.