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.
Highlights
In a series of recent works [6, 7, 8, 11, 12] several authors have developed a design framework based on the Fisher Information Matrix (FIM) for a system of differential equations to determine when and where an experimenter should take samples and what variables to measure in collecting information on a physical or biological process that is modeled by a vector dynamical system
This framework has been proposed for use in inverse problem methodologies in the context of dynamical system or mathematical model parameter estimation when one investigates the sufficiency of the number of observations of one or more states
We have shown the value of using some type of optimal design criterion in determining how to best collect data
Summary
The fundamental problem of collecting data in the est way" in order to assure statistically e cient 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 ts to measured data. We consider an electromagnetic interrogation problem, speci cally one arising in an electroencephalography (EEG) problem, of nding optimal number and locations for sensors for source identi cation in a 3D unit sphere from data on its boundary. In this e ort we compare the use of the classical D-optimal criterion for observation points as opposed to that for a uniform observation mesh.
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