Optimal linear reduced-rank estimation

Summary form only given. The problem of estimating an unknown signal or property vector, x∈R^p, from a multichannel data vector z∈Rⁿ, p ⩽n, by means of a linear estimator having rank ⩽ p is considered. Here, x and z are treated as stochastic variables characterized by their first- and second-order statistics. A reduced-rank linear transformation of z that provides an estimate of z minimizing a (weighted) mean-square-error cost function is sought. Typically, z will represent a noisy data vector and possibly also contain extraneous coherent components; x can represent either the noise-free signal of interest or a set of quantities related to the signal, such as the underlying physical properties which determine the signal, in which case the problem is one of data inversion. The result can be viewed as a synthesis of the Karhunen-Loeve transformation with linear mean-square estimation, and thus as a generalization of each