Inhalt des Dokuments
|Dr. Tomasz Piotrowski, Nicolaus Copernicus
|Friday, September 6, 2013, 12 a.m., room HFT
Reduced-rank approach has been in continuous use in signal processing for decades, as it achieves much reduced variance in ill-conditioned estimation than full-rank estimators, at the expense of introducing small amount of bias. In this talk I will introduce the minimum-variance pseudo-unbiased reduced-rank estimation (MV-PURE) framework as the reduced-rank approach with well-defined optimality properties in the sense of minimizing MSE among estimators of predefined rank. In particular, I will show the exact conditions under which MV-PURE achieves lower MSE than linear minimum MSE estimator (Wiener filter), if channel perturbation is introduced in the y=Hx+n model. I will also show that the MV-PURE approach is recognized as a natural extension of the celebrated linearly-constrained minimum-variance beamformer, which opens new areas of application of MV-PURE. The talk will close with introduction of a new MV-PURE-based approach to source localization in electroencephalography (EEG) and magnetoencephalography (MEG), which possesses rather surprising optimality properties, and allows for much more precise source localization than existing state-of-the-art methods if the EEG/MEG forward model becomes ill-conditioned.
Tomasz Jan Piotrowski was born in Poland in 1980. He received the MSc degree in Mathematics from Silesian University of Technology, Poland, in 2004, the MSc degree in Information Processing & Neural Networks from King’s College London, UK, in 2005, and the PhD degree in Communications and Integrated Systems from Tokyo Institute of Technology, Japan, in 2008. From 2009 to 2010 he worked at Comarch SA, Poland, on mining large data sets in multidimensional databases. From 2011 he has been with the Nicolaus Copernicus University, Department of Informatics, Faculty of Physics, Astronomy, and Informatics, Poland. His current interest is in biomedical signal processing.