Mathematical Biosciences and Engineering (MBE)

Optimal design for parameter estimation in EEG problems in a 3D multilayered domain

Pages: 739 - 760, Volume 12, Issue 4, August 2015      doi:10.3934/mbe.2015.12.739

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H. T. Banks - Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212, United States (email)
D. Rubio - Centro de Matemática Aplicada, Universidad de San Martín, Buenos Aires, Argentina (email)
N. Saintier - Instituto de Ciencias, Universidad Nacional Gral. Sarmiento, Buenos Aires, Argentina (email)
M. I. Troparevsky - Dep. de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires, Argentina (email)

Abstract: The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical $D$-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters.

Keywords:  Electromagnetic inverse problems, optimal design in 3D EEG analysis, parameter estimation, asymptotic error analysis.
Mathematics Subject Classification:  62F12, 62K05, 65M32.

Received: April 2014;      Accepted: December 2014;      Available Online: April 2015.