Ebook Brain source localization using EEG signal analysis: Part 2
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Ebook Brain source localization using EEG signal analysis: Part 2
chapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2rain source localization using non invasive measurements of brain activities, such as EEG and magnetoencephalography (MEG). Brain source localization uses measurements of the voltage potential or magnetic field at various locations on the scalp and then estimates the current sources inside the brain Ebook Brain source localization using EEG signal analysis: Part 2 that best fit these data using different estimators.The earliest efforts to quantify the locations of the active EEG sources in the brain occurred moEbook Brain source localization using EEG signal analysis: Part 2
re than 50 years ago when researchers began to relate their electrophysiological knowledge about the brain to the basic principles of volume currents chapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2he medium, which lead to potential differences on its surface. Given the special structure of the pyramidal cells in the cortical area, if enough of these cells are in synchrony, volume currents large enough to produce measurable potential differences on the scalp will be generated.The process of ca Ebook Brain source localization using EEG signal analysis: Part 2lculating scalp potentials from current sources inside the brain is generally called the forward problem. If the locations of the current sources in tEbook Brain source localization using EEG signal analysis: Part 2
he brain are known and the conductive properties of the tissues within the volume of the head are also known, the potentials on the scalp can be calcuchapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2e scalp potentials is called the inverse problem.Source localization is an inverse problem, where a unique relationship between the sea Ip-recorded EEG and neural sources may not exist. Therefore, different source models have been investigated. However, it is well established that neural activity ca Ebook Brain source localization using EEG signal analysis: Part 2n be modeled using equivalent current dipole models to represent well-localized activated neural sources [4,5].Numerous studies have demonstrated a nuEbook Brain source localization using EEG signal analysis: Part 2
mber of applications of dipole source localization in clinical medicine and neuroscience research, and many algorithms have been developed to estimatechapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2hods have received considerable attention because of their ability to accurately locate multiple closely spaced dipole sources and/or correlated dipoles. In principle, subspace-based methods find (maximum) peak locations of their cost functions as source locations by employing certain projections on Ebook Brain source localization using EEG signal analysis: Part 2to the estimated signal subspace, or alternatively, onto the estimated noise-only subspace (the orthogonal complement of the estimated signal subspaceEbook Brain source localization using EEG signal analysis: Part 2
), which are obtained from the measured EEG data. The subspace methods that have been studied for MEG/EEG include classic multiple signal classificatichapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2osher et al. [4] pioneered the investigation of MEG source dipole localization by adapting the MUSIC algorithm, which was initially developed for radar and sonar applications [8). Their work has made an influential impact on the field, and MUSIC has become one of most popular approaches in MEG/EEG s Ebook Brain source localization using EEG signal analysis: Part 2ource localization. Extensive studies in radar and sonar have shown that MUSIC typically provides biased estimates when sources are weak or highly corEbook Brain source localization using EEG signal analysis: Part 2
related [9Ị. Therefore, other subspace algorithms that do not provide large estimation bias may outperform MUSIC in the case of weak and/or correlatedchapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2 (ID) linear array simulations that when sources were highly correlated, RAP-MUSIC had better source resolvability and smaller root mean-squared error of location estimates as compared with classic MUSIC.In 2003, Xu et al. [10] proposed a new approach to EEG three-dimensional (3D) dipole source loca Ebook Brain source localization using EEG signal analysis: Part 2lization using a nonrecursive subspace algorithm called first principle vectors (FINES). In estimating source dipole locations, the present approach eEbook Brain source localization using EEG signal analysis: Part 2
mploys projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of thechapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2st to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanc Ebook Brain source localization using EEG signal analysis: Part 2ed accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors.In this chapter,Ebook Brain source localization using EEG signal analysis: Part 2
we outline the MUSIC and its variant, the RAP-MUSIC algorithm, and the FINES as representatives of the subspace techniques in solving the inverse probchapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2 methods that do notChapter seven: EEG inverse problem III93impose specific constraints on the form of the array manifold. For this reason, we do not consider methods such as estimation of signal parameters via rotational invariance techniques (ESPRIT) [11] or root multiple signal classification-MUS Ebook Brain source localization using EEG signal analysis: Part 2IC (ROOT-MUSIC), which exploits shift invariance or Vandermonde structure in specialized arrays.Subspace methods have been widely used in applicationsEbook Brain source localization using EEG signal analysis: Part 2
related to the problem of direction of arrival estimation of far-field narrowband sources using linear arrays. Recently, subspace methods started to chapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2magnetic fields, namely, EEG or MEG signals [6]. These current dipoles represent the foci of neural current sources in the cerebral cortex associated with neural activity in response to sensory, motor, or cognitive stimuli. In this case, the current dipoles have three unknown location parameters and Ebook Brain source localization using EEG signal analysis: Part 2 an unknown dipole orientation. A direct search for the location and orientation of multiple sources involves solving a highly nonconvex optimizationEbook Brain source localization using EEG signal analysis: Part 2
problem.One of the various approaches that can be used to solve this problem is die MUSIC [8Ị algorithm. The main attractions of MUSIC are that it canchapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2 space for each source, avoiding the local minima problem, which can be faced while searching for multiple sources over a nonconvex error surface. However, two problems related to MUSIC implementation often arise in practice. The first one is related to die errors in estimating the signal subspace, Ebook Brain source localization using EEG signal analysis: Part 2which can make it difficult to differentiate "true" from "false" peaks. The second is related to the difficulty in finding several local maxima in theEbook Brain source localization using EEG signal analysis: Part 2
MUSIC algorithm because of the increased dimension of the source space. To overcome these problems, the RAP-MUSIC and FINES algorithms were introducechapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2 forward problem is briefly described, followed with a detailed discussion of the MUSIC, the RAP-MUSIC, and the FINES algorithms.7.1Fundamentals of matrix subspaces7.1.1Vector subspaceConsider a set of vectors s in the //-dimension real space R".s is a subspace of R” if it satisfies the following pr Ebook Brain source localization using EEG signal analysis: Part 2operties:•The zero vector € s.•s is closed under addition. This means that if u and V are vectors in s, then their sum u + V must be in s.•s is closedEbook Brain source localization using EEG signal analysis: Part 2
under scalar multiplication. This means that if u is a vector in H and c is any scalar, the product cu must be in s.94Brain source localization usingchapter sevenEEG inverse problem IIISubspace-based techniquesIntroductionOver the past few decades, a variety of techniques have been developed for br Ebook Brain source localization using EEG signal analysis: Part 2 linear combination of the others:n0 implies n(1:/i) 0/=1-7.1Gọi ngay
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