EEG source localization by multi-planar analytic sensing

Kandaswamy, D.; Blu, Thierry; Spinelli, Laurent; Michel, Christoph M.; Ville, Dimitri Van De

doi:10.1109/isbi.2008.4541186

Cited by 2 publications

(5 citation statements)

References 8 publications

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“…We have shown how to efficiently localize point sources in the 2D case; we will show how we can adapt the proposed method for the 3D case. Basically, we can account for a z-component using two approaches: a multiplanar approach [11] and the use of a second set of test functions to reconstruct the missing z-component. Here we exploit the second approach, because we find it more consistent with our analytic sensing theory.…”

Section: Resultsmentioning

confidence: 99%

“…(11) More specifically, we will restrict further our choice of a n to the form a n = a 0 e inα , where…”

Section: 2mentioning

confidence: 99%

“…We term our method "analytic sensing" because it relies heavily on a careful choice of analytic test functions-sensors [10,11,12]. Our contributions are twofold:…”

mentioning

confidence: 99%

“…The first set {ψ an } an / ∈Ω contains the same sensors 3 as described in (11); that is, ψ an (x, y, z) = 1 x+iy−an . Next, we apply the algorithm as schematized in Figure 4.…”

mentioning

confidence: 99%

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Analytic Sensing: Noniterative Retrieval of Point Sources from Boundary Measurements

Kandaswamy¹,

Blu²,

Ville³

2009

SIAM J. Sci. Comput.

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Abstract. We consider the problem of locating point sources in the planar domain from overdetermined boundary measurements of solutions of Poisson's equation. In this paper, we propose a novel technique, termed "analytic sensing," which combines the application of Green's theorem to functions with vanishing Laplacian-known as the "reciprocity gap" principle-with the careful selection of analytic functions that "sense" the manifestation of the sources in order to determine their positions and intensities. Using this formalism we express the problem at hand as a generalized sampling problem, where the signal to be reconstructed is the source distribution. To determine the positions of the sources, which is a nonlinear problem, we extend the annihilating-filter method, which reduces the problem to solving a linear system of equations for a polynomial whose roots are the positions of the point sources. Once these positions are found, resolving the according intensities boils down to solving a linear system of equations. We demonstrate the performance of our technique in the presence of noise by comparing the achieved accuracy with the theoretical lower bound provided by Cramér-Rao theory. 1. Introduction. Source imaging from boundary Cauchy data satisfying the Laplace equation is a classical inverse problem that is of high interest to many fields in engineering. Unfortunately, the problem is ill-posed and additional assumptions about the source configuration are needed to make the solution unique. Typically, one can restrict the class of source distributions by imposing smoothness properties (e.g., Tikhonov regularization [19]) or by imposing a parametric source model.It is when the source configurations are expected to be "sparse" that parametric solutions may prove very useful. This situation is particularly attractive in the electromagnetic setting for applications such as electroencephalography (EEG); e.g., the localization of some type of epileptic foci can be reasonably modeled by pointwise (dipolar) sources [15]. Almost all known techniques rely on the forward model; i.e., computing the boundary data for a given source configuration and iteratively fitting its parameters by least-squares optimization [16]. The corresponding cost function has many local minima and makes the solution very sensitive to the initial guess. Therefore, successful recovery of the parametric sources is often limited to single-dipole models.Despite the practical difficulties in identifying parametric source models, the mathematical uniqueness of the solution has been proven [7], and stability results are available for the case of dipolar and point sources in 2D [5,16] and 3D [20]. Instead

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Section: Resultsmentioning

confidence: 99%

“…(11) More specifically, we will restrict further our choice of a n to the form a n = a 0 e inα , where…”

Section: 2mentioning

confidence: 99%

“…We term our method "analytic sensing" because it relies heavily on a careful choice of analytic test functions-sensors [10,11,12]. Our contributions are twofold:…”

mentioning

confidence: 99%

“…The first set {ψ an } an / ∈Ω contains the same sensors 3 as described in (11); that is, ψ an (x, y, z) = 1 x+iy−an . Next, we apply the algorithm as schematized in Figure 4.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Analytic Sensing: Noniterative Retrieval of Point Sources from Boundary Measurements

Kandaswamy¹,

Blu²,

Ville³

2009

SIAM J. Sci. Comput.

Self Cite

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“…This problem is modified by the proposed method to find the polynomial roots. However, the computational cost of this method is very high, which reduces the possibility of online implementation [65]. In 2008, one technique was proposed which localizes source activity using a linear mixture of temporal basis functions (TBFs) learned from data.…”

Section: Solving the Inverse Problem By Statistical Methodsmentioning

confidence: 99%

A systematic review of EEG source localization techniques and their applications on diagnosis of brain abnormalities

Asadzadeh

Rezaii

Beheshti

et al. 2020

Journal of Neuroscience Methods

107

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In recent years, multiple noninvasive imaging modalities have been used to develop a better understanding of the human brain functionality, including positron emission tomography, single-photon emission computed tomography, and functional magnetic resonance imaging, all of which provide brain images with millimeter spatial resolutions. Despite good spatial resolution, time resolution of these methods are poor and values are about seconds. Electroencephalography (EEG) is a popular non-invasive electrophysiological technique of relatively very high time resolution which is used to measure electric potential of brain neural activity. Scalp EEG recordings can be used to perform the inverse problem in order to specify the location of the dominant sources of the brain activity. In this paper, EEG source localization research is clustered as follows: solving the inverse problem by statistical method (37.5%), diagnosis of brain abnormalities using common EEG source localization methods (18.33%), improving EEG source localization methods by non-statistical strategies (3.33%), investigating the effect of the head model on EEG source imaging results (12.5%), detection of epileptic seizures by brain activity localization based on EEG signals (20%), diagnosis and treatment of ADHD abnormalities (8.33%). Among the available methods, minimum norm solution has shown to be very promising for sources with different depths. This review investigates diseases that are diagnosed using EEG source localization techniques. In this review we provide enough evidence that the effects of psychiatric drugs on the activity of brain sources have not been enough investigated, which provides motivation for consideration in the future research using EEG source localization methods.Index Terms-EEG signals, source localization, the inverse problem, head model, brain abnormalities, time resolution.S. Beheshti is with the

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EEG source localization by multi-planar analytic sensing

Cited by 2 publications

References 8 publications

Analytic Sensing: Noniterative Retrieval of Point Sources from Boundary Measurements

Analytic Sensing: Noniterative Retrieval of Point Sources from Boundary Measurements

A systematic review of EEG source localization techniques and their applications on diagnosis of brain abnormalities

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