Comparison of EEG source localization using meromorphic approximation to fuzzy C-mean


  • Leila Saeidias
  • Tahir Ahmad
  • Norma Alias
  • Mehdi ghanbari



EEG source localization, Meromorphic Function, Fuzzy c-means,


Electroencephalography (EEG) is a neuroimaging technique for localizing active sources within the brain, from knowledge of electromagnetic
measurements outside the head. Recognition of point sources from boundary measurements is an ill-posed inverse problem. InEEG, measurements are
only accessible at electrode positions, the number of sources is not known a prior. This paper proposes a comparison between two approaches for EEG
source localization. First method based on Meromorphic approximation techniques in the complex plane and second one belongs to EEG’s method
which is processed using Fuzzy C-Means (FCM). Comparison results on simulated data are used to verify the superior of the Meromorphic
approximation with regarding to Fuzzy c-means, due to it provides the way for solving inverse problem of EEG source localization in 3D from boundary
measurement based on Harmon function in the innermost layer .


S .Vessella, Inverse Problems, 8.6 (1992) 911–9117.

V .Isakov, Inverse Problems for Partial Differential Equations,

Springer, USA, 1998.

R. D. Pascual-Marqui, ISBET Newslett, 6 (1995) 16–28.

A.El Badia, and T.Ha-Duong, Inverse Problems, 16 (2000) 651–

M .Scherg, T. Bast, and P .Berg, J. Clin. Neurophysiol. 16 (1999)


B. Cuffin, IEEE Trans. Biomed. Eng., 42 (1995) 68–71.

C.G .B´enar, R. N.Gunn, C.Grova, B.Champagne , and J.Gotman

,IEEE Trans. Biomed. Eng., 52 (2005) 401–413.

J .C .Mosher, P. S .Lewis, and R .M. Leahy, IEEE Trans. Biomed.

Eng., 39 (1992) 541–553.

A.Bahramisharif, M. A.J. Gerven, J.M. Schoffelen, Z.Ghahramani,

and T. Heskes, Machine Learning and Interpretation in

Neuroimaging. Springer Berlin Heidelberg, 2012, 148-155.

B. D. Van Veen, and K .M .Buckley, IEEE Acoust. Speech Signal

Process Mag., 5 (1988) 4–24.

M. Clerc, J .Leblond , J. P. M,armorat, and T. Papadopoulo, Inverse

Problems, 28 (2012) 1-24.

J.C .Bezdek, Pattern Recognition with Fuzzy Objective Function

Algorithms. Plenum Press, New York, 1981.

J.C .Dunn, and J.Cybern, 3 (1974) 32-57.

M .Clerc , and J .Kybic. , Inverse Problems 23 (2007) 589–601.

L .Baratchart, J .Leblond , and J.P. Marmorat, Electron. Trans.

Numer. Anal., 25(2006) 41–53.

J .Leblond, C .Paduret, S .Rigat and M. Zghal, Inverse Problems 24

(2008) 1-38.

R .Bassila, M .Clerc, J .Leblond, J.P. Marmorat and T. Papadopoulo,

FindSources3D software, http://wwwsop., (2008).

J .Kybic, M .Clerc, T .Abboud, O .Faugeras, R .Keriven and T.

Papadopoulo , IEEE Trans. Med. Imaging, 24 (1965)12–28.

L.A. Zadeh, 8 (1965) 338-353.

F .Zakaria, PhD Thesis, Universiti Teknologi Malaysia, 2008.

F .Tadel, S .Baillet, J.C .Mosher, D .Pantazis, R.M.

Leahy, Computational intelligence and neuroscience, 2011 (2011)


A. Gramfort, T. Papadopoulo, E. Olivi, and M. Clerc. Biomedical

Engineering Online 9 (2010) 1-20.