Research - MV-PURE

The minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE) by Yamada and Elbadraoui (2006), by Piotrowski and Yamada (2008), was established as a novel reduced-rank extension of the celebrated Gauss-Markov (BLUE) estimator for ill-conditioned linear inverse problems. The MV-PURE is defined as a closed form solution of a hierarchical nonconvex constrained optimization problem and achieves the minimum variance among all solutions of the first stage optimization problem for minimizing, under a rank constraint, simultaneously all unitarily invariant norms of an operator applied to the unknown parameter vector in view of suppressing bias of the estimator.

Building on the MV-PURE approach, the stochastic MV-PURE estimator by Piotrowski, Cavalcante, and Yamada (2009), aims at robust estimation of an unknown random vector of parameters in highly noisy and ill-conditioned settings with imperfect model knowledge, where the theoretically optimal in the mean-square-error sense linear estimator (Wiener filter) has a much degraded performance in such settings. The stochastic MV-PURE estimator is a solution of a similar optimization problem to the deterministic MV-PURE, but in the stochastic case we are able to minimize directly the mean-square-error in the second stage optimization.

RR-NAIs recently developed in our group are unbiased and have higher spatial resolution than their full-rank counterparts in challenging task of localizing closely positioned and possibly highly correlated sources, especially in low signal-to-noise regime.