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 of pursue learn in both the engineering or the neuroscientific points of electromagnetic mind imaging. This textbook won't basically entice graduate scholars yet all scientists and engineers engaged in study on electromagnetic mind imaging.
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Additional resources for Electromagnetic Brain Imaging: A Bayesian Perspective
Example text
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. Thus, we have p(x k |α) = N (x k |0, Φ −1 N )= N (x j |0, α−1 j ). 5) j=1 Since we assume that the noise ε is independent across time, the conditional probability p( y|x) is expressed as K p( y|x) = K p( yk |x k ) = k=1 N ( yk |H x k , β −1 I). 6) k=1 In this chapter, the noise precision matrix is assumed to be β I where β is known.
3 Problem with Source Orientation Estimation When applying the L 1 -norm regularization to the bioelectromagnetic source localization, it has been known that the method fails in estimating correct source orientations. The reason for this is described as follows: The components of the solution vector x is denoted explicitly as y y y x = s1x , s1 , s1z , . . , s xj , s j , s zj , . . , s Nx , s N , s Nz T , y where s xj , s j , s zj are the x, y, and z components of the source at the jth voxel.
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