Electromagnetic Brain Imaging: A Bayesian Perspective by Kensuke Sekihara, Srikantan S. Nagarajan

By Kensuke Sekihara, Srikantan S. Nagarajan

This graduate point textbook presents a coherent advent to the physique of main-stream algorithms utilized in electromagnetic mind imaging, with particular emphasis on novel Bayesian algorithms. It is helping readers to extra simply comprehend literature in biomedical engineering and comparable fields and be capable to pursue study in both the engineering or the neuroscientific features of electromagnetic mind imaging. This textbook won't merely entice graduate scholars yet all scientists and engineers engaged in study on electromagnetic mind imaging.

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X K and the whole sensor time series y1 , y2 , . . , y K . We first formulate the Champagne algorithm omitting the source orientation estimation. That is, we assume that the source orientation is predetermined at each voxel and use the measurement model in Eq. 15). 3) where the lead field matrix H is defined in Eq. 11). 2 Probabilistic Model and Method Formulation Defining a column vector α such that α = [α1 , . . 4) k=1 where Φ is equal to Φ = diag(α), which indicates a diagonal matrix whose diagonal elements are those of a vector in the parenthesis.

Therefore, the minimum-norm method in Eq. 26) generally produces results highly susceptible to the noise in the sensor data. 8 L 2 -Regularized Minimum-Norm Solution When a large amount of noise is overlapped onto the sensor data y, if we seek a solution that satisfies y = Fx, the resultant solution x would be severely affected by the noise. In other words, when noise exists in the sensor data, it is more or less 3 Computing the lead field using the spherical homogeneous conductor model is explained in Sect.

E. Tipping, Sparse Bayesian learning and relevance vector machine. J. Mach. Learn. Res. 1 Introduction and Basic Formulation The beamformer is a location-dependent spatial filter applied to the sensor data. It is used for estimating the strength of brain activity at a particular spatial location, which is referred to as the beamformer pointing location. Thus, the beamformer may be interpreted as a technique that forms a virtual sensor whose sensitivity pattern is localized at its pointing location.

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