Inverse electroencephalography for cortical sources

Fraguela, A.; Óliveros, J.; Morín, M.; Cervantes, L.

doi:10.1016/j.apnum.2005.02.004

Cited by 11 publications

(15 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The latter problem involves determining the source that yields the measurement on the boundary of the region [12][13][14]. The inverse source problem appears in different applications, such as inverse electroencephalography, inverse electrocardiography and inverse geophysics (see, e.g., [15][16][17][18][19][20][21][22][23]), where the problems are modeled using differential equations. Numerical solutions to differential equations are crucial in mathematics and engineering because they appear in many applications, such as population growth, diffusion processes, electromagnetic problems, and elasticity problems.…”

Section: Introductionmentioning

confidence: 99%

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

et al. 2021

View full text Add to dashboard Cite

This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.

show abstract

Section: Introductionmentioning

confidence: 99%

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In the case of sources that have support in a manifold of dimension one or two or in the case of dipolar sources, we must make other analysis [6].…”

Section: Introductionmentioning

confidence: 99%

“…[4][5][6]. The simple case in which the source is represented by a finite number of dipoles is studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Inverse electroencephalography for volumetric sources

Collar

Castillo

Óliveros

2008

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

“…The Cauchy problem is important in many applications like estimating the deterioration of a pipeline, calculating a solution or “potential” in some regions or on boundaries where there is no direct access, and finding cracks on plates . It is also important for applications in some areas such as Geophysics, tomography of processes, inverse electroencephalography, and inverse electrocardiography .…”

Section: Introductionmentioning

confidence: 99%

Stable numerical solution of the Cauchy problem for the Laplace equation in irregular annular regions

Mones

Valencia

Óliveros

et al. 2017

Numerical Methods Partial

View full text Add to dashboard Cite

This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace equation in a bounded annular region. To solve this ill‐posed problem, we follow a variational approach based on its reformulation as a boundary control problem, for which the cost function incorporates a penalized term with the input data. The cost function is minimized by a conjugate gradient method in combination with a finite element discretization. In the case where the input data is noisy, some preliminary error estimates, show that the penalization parameter may be chosen like the inverse of the level of noise. Numerical solutions in simple and complex domains show that this methodology produces stable and accurate solutions.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1799–1822, 2017

show abstract

Inverse electroencephalography for cortical sources

Cited by 11 publications

References 10 publications

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

Inverse electroencephalography for volumetric sources

Stable numerical solution of the Cauchy problem for the Laplace equation in irregular annular regions

Contact Info

Product

Resources

About