| Paper: | SPTM-P3.5 | ||
| Session: | System Modeling, Representation and Identification | ||
| Time: | Tuesday, May 16, 16:30 - 18:30 | ||
| Presentation: | Poster | ||
| Topic: | Signal Processing Theory and Methods: System Modeling, Representation, and Identification | ||
| Title: | Minimum-Variance Pseudo-Unbiased Low-Rank Estimator for Ill-Conditioned Inverse Problems | ||
| Authors: | Isao Yamada, Jamal Elbadraoui, Tokyo Institute of Technology, Japan | ||
| Abstract: | This paper presents a mathematically novel low-rank linear statistical estimator named minimum-variance pseudo-unbiased low-rank estimator for applications to ill-conditioned linear inverse problems. Based on a simple fact: `any low-rank estimator can not be a (uniformly) unbiased estimator', we introduce pseudo-unbiased low-rank estimator, as an ideal low-rank extension of unbiased estimators. The minimum-variance pseudo-unbiased low-rank estimator minimizes the variance of estimate among all pseudo-unbiased low-rank estimators, hence it is characterized as a solution to a double layered nonconvex optimization problem. The main theorem presents an algebraic structure of the minimum-variance pseudo-unbiased low-rank estimator in terms of the singular value decomposition of the model matrix in the linear statistical model. The minimum-variance pseudo-unbiased low-rank estimator is not only a best low-rank extension of the minimum-variance unbiased estimator (i.e., Gauss-Markov estimator) but also a nontrivial generalization of the Marquardt's low-rank estimator (Marquardt 1970). | ||
©2018 Conference Management Services, Inc. -||- email: webmaster@icassp2006.org -||- Last updated Friday, August 17, 2012