EEG inverse problem III
Munsif Ali Jatoi, Nidal Kamel · 2017
This chapter discusses one of the important classes of source localization techniques, which are based on subspace. Hence, a thorough and detailed account is provided on all the subspace-based brain source localization techniques. For this, initially the basic concepts associated with subspace concepts are demonstrated with the help of basic linear algebra. The discussion provides fundamentals of matrix subspaces, which include linear independence, span of vectors, basis of subspace, orthogonal and orthonormal vectors, singular-value decomposition (SVD) and symmetric eigenvalue decomposition (EVD). After which, a simple discussion is provided to revisit the forward problem. Moreover, the SVD-based algorithms such as MUSIC and RAP MUSIC are discussed in detail. Finally, First Principle Vectors (FINES) algorithm is discussed to support the discussion for the subspace-based source localization algorithms.