Rate-distortion trade-offs in acquisition of signal parameters

We consider problems where one wishes to represent a parameter associated with a signal source - subject to a certain rate and distortion - based on the observation of a number of realizations of the source signal. By reducing these indirect vector quantization problems to a standard vector quantization one, we provide a bound to the fundamental interplay between the rate and distortion in the large-rate setting. We specialize this characterization to two particular quantization scenarios: i) the representation of the mean of a multivariate Gaussian source; and ii) the representation of the eigen-spectrum of a multivariate Gaussian source. Numerical results compare our quantization approach to an approach where one recovers the parameters from the representation of the source signals itself: in addition to revealing that the characterization is sharp in the large-rate setting, the results also show that our approach offers considerable gains.