SPHARA - A generalized spatial fourier analysis for multi-sensor systems with non-uniformly arranged sensors: Application to EEG

PLoS ONE

Volumn 10, Issue 4, 2015, Pages

  Graichen, Uwe ^a   Eichardt, Roland ^a   Fiedler, Patrique ^a   Strohmeier, Daniel ^a   Zanow, Frank ^b   Haueisen, Jens ^a,c  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

^b Eemagine GmbH   (Germany)

^c University Clinic Jena   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BASIS FUNCTION; COMPARATIVE STUDY; DIMENSIONALITY REDUCTION; ELECTROENCEPHALOGRAM; EVOKED SOMATOSENSORY RESPONSE; FINITE ELEMENT ANALYSIS; FOURIER ANALYSIS; HUMAN; IMAGE PROCESSING; INDEPENDENT COMPONENT ANALYSIS; LAPLACE BELTRAMI OPERATOR; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL PHENOMENA; NOISE REDUCTION; PRINCIPAL COORDINATE ANALYSIS; SENSOR; SIGNAL NOISE RATIO; SPATIAL DATA DECOMPOSITION; SPATIAL HARMONIC ANALYSIS; TIME SERIES ANALYSIS; ADULT; ALGORITHM; BRAIN; BRAIN MAPPING; ELECTROENCEPHALOGRAPHY; MALE; PHYSIOLOGY;

ADULT; ALGORITHMS; BRAIN; BRAIN MAPPING; ELECTROENCEPHALOGRAPHY; FOURIER ANALYSIS; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MALE; SIGNAL-TO-NOISE RATIO;

EID: 84929485548     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0121741     Document Type: Article

References (54)

1. Rao K, Kim D, Hwang J (2010) Fast Fourier Transform: Algorithms and Applications. Signals and communication technology. Springer.
2. Bashashati A, Fatourechi M, Ward RK, Birch GE (2007) A survey of signal processing algorithms in brain-computer interfaces based on electrical brain signals. Journal of Neural Engineering 4: R32-R57. doi: 10.1088/1741-2560/4/2/R03 PMID: 17409474
3. Brunner C, Naeem M, Leeb R, Graimann B, Pfurtscheller G (2007) Spatial filtering and selection of optimized components in four class motor imagery EEG data using independent components analysis. Pattern Recognition Letters 28: 957-964. doi: 10.1016/j.patrec.2007.01.002
4. Pourtois G, Delplanque S, Michel C, Vuilleumier P (2008) Beyond conventional event-related brain potential (ERP): Exploring the time-course of visual emotion processing using topographic and principal component analyses. Brain Topography 20: 265-277. doi: 10.1007/s10548-008-0053-6 PMID: 18338243
5. Soong ACK, Koles ZJ (1995) Principal-component localization of the sources of the background EEG. IEEE Transactions on Biomedical Engineering 42: 59-67. doi: 10.1109/10.362918 PMID: 7851931
6. Koles ZJ, Lind JC, Soong ACK (1995) Spatio-temporal decomposition of the EEG: a general approach to the isolation and localization of sources. Electroencephalography and clinical Neurophysiology 95: 219-230. doi: 10.1016/0013-4694(95)00083-B PMID: 8529553
7. Lagerlund TD, Sharbrough FW, Busacker NE (1997) Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition. Journal of Clinical Neurophysiology 14: 73-82. doi: 10.1097/00004691-199701000-00007 PMID: 9013362
8. Bell A, Sejnowski T (1995) An information-maximization approach to blind separation and blind deconvolution. NEURAL COMPUTATION 7: 1129-1159. doi: 10.1162/neco.1995.7.6.1129 PMID: 7584893
9. Hyvärinen A, Oja E (2000) Independent component analysis: algorithms and applications. Neural Networks 13: 411-430. doi: 10.1016/S0893-6080(00)00026-5 PMID: 10946390
10. Jung TP, Makeig S, Westerfield M, Townsend J, Courchesne E, Sejnowski TJ (2001) Analysis and visualization of single-trial event-related potentials. Human Brain Mapping 14: 166-185. doi: 10.1002/hbm.1050 PMID: 11559961
11. Delorme A, Makeig S (2004) EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. Journal of Neuroscience Methods 134: 9-21. doi: 10.1016/j.jneumeth.2003.10.009 PMID: 15102499
12. Hyvärinen A, Karhunen J, Oja E (2001) Independent Component Analysis. Wiley-Interscience, 1st edition.
13. De Lucia M, Michel CM, Murray M (2010) Comparing ica-based and single-trial topographic erp analyses. Brain Topography 23: 119-127. doi: 10.1007/s10548-010-0145-y PMID: 20422446
14. Serby H, Yom-Tov E, Inbar GF (2005) An improved P300-based brain-computer interface. IEEE Transactions on Neural Systems and Rehabilitation Engineering 13: 89-98. doi: 10.1109/TNSRE.2004.841878 PMID: 15813410
15. Bayliss J, Ballard D (2000) A virtual reality testbed for brain-computer interface research. IEEE Transactions on Rehabilitation Engineering 8: 188-190. doi: 10.1109/86.847811 PMID: 10896182
16. Miwakeichi F, Martinez-Montes E, Valdes-Sosa PA, Nishiyama N, Mizuhara H, Yamaguchia Y (2004) Decomposing EEG data into space-time-frequency components using parallel factor analysis. Neuroimage 22: 1035-1045. doi: 10.1016/j.neuroimage.2004.03.039 PMID: 15219576
17. Morup M, Hansen LK, Herrmann CS, Parnas J, Arnfred SM (2006) Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG. Neuroimage 29: 938-947. doi: 10.1016/j.neuroimage.2005.08.005 PMID: 16185898
18. Cichocki A, Washizawa Y, Rutkowski T, Bakardjian H, Phan AH, Choi S, et al. (2008) Noninvasive BCIs: Multiway signal-processing array decompositions. Computer 41: 34-42. doi: 10.1109/MC.2008.431
19. Durka PJ, Blinowska KJ (1995) Analysis of EEG transients by means of matching pursuit. Annals of Biomedical Engineering 23: 608-611. doi: 10.1007/BF02584459 PMID: 7503462
20. Durka P, Matysiak A, Martinez Montes E, Valdes Sosa P, Blinowska K (2005) Multichannel matching pursuit and EEG inverse solutions. Journal of Neuroscience Methods 148: 49-59. doi: 10.1016/j.jneumeth.2005.04.001 PMID: 15908012
21. Gratkowski M, Haueisen J, Arendt-Nielsen L, Zanow F (2007) Topographic matching pursuit of spatiotemporal bioelectromagnetic data. Przeglad Elektrotechniczny 83: 138-141.
22. Gratkowski M, Haueisen J, Arendt-Nielsen L, Chen ACN, Zanow F (2008) Decomposition of biomedical signals in spatial and time-frequency modes. Methods of Information in Medicine 47: 26-37. PMID: 18213425
23. Wingeier BM, Nunez PL, Silberstein RB (2001) Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density electroencephalogram. Physical Review E 64: 14941-14962. doi: 10.1103/PhysRevE.64.051916
24. Chung FRK (1997) Spectral Graph Theory, volume 92. American Mathematical Society. CBMS Regional Conference Series in Mathematics.
25. Taubin G (2000) Geometric signal processing on polygonal meshes. In: Coquillart S, Duke D, editors, STAR Proceedings of Eurographics 2000. Eurographics Association.
26. Zhang H, van Kaick O, Dyer R (2007) Spectral methods for mesh processing and analysis. In: Schmalstieg D, Bittner J, editors, STAR Proceedings of Eurographics. volume 92, pp. 1-22.
27. Reuter M, Wolter FE, Peinecke N (2006) Laplace-beltrami spectra as 'Shape-DNA' of surfaces and solids. Computer-Aided Design 38: 342-366. doi: 10.1016/j.cad.2005.10.011
28. Haines GV (1988) Computer-programs for spherical cap harmonic-analysis of potential and general fields. Computers & Geosciences 14: 413-447. doi: 10.1016/0098-3004(88)90027-1
29. De Santis A (1991) Translated origin spherical cap harmonic analysis. Geophysical Journal International 106: 253-263. doi: 10.1111/j.1365-246X.1991.tb04615.x
30. Bradshaw LA, Wikswo JP (2001) Spatial filter approach for evaluation of the surface laplacian of the electroencephalogram and magnetoencephalogram. Annals of Biomedical Engineering 29: 202-213. doi: 10.1114/1.1352641 PMID: 11310782
31. Nunez PL, Westdorp AF (1994) The surface laplacian, high resolution EEG and controversies. Brain Topography 6: 221-226. doi: 10.1007/BF01187712 PMID: 8204409
32. Nunez PL, Silberstein RB, Cadusch PJ, Wijesinghe RS, Westdorp AF, Srinivasan R, et al. (1994) A theoretical and experimental study of high resolution EEG based on surface laplacians and cortical imaging. Electroencephalography and Clinical Neurophysiology 90: 40-57. doi: 10.1016/0013-4694(94)90112-0 PMID: 7509273
33. Gramfort A, Clerc M (2007) Low dimensional representations of MEG/EEG data using laplacian eigen-maps. In: Joint Meeting of the 6th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the International Conference on Functional Biomedical Imaging. pp. 169-172.
34. Ramirez-Velez M, Staba R, Barth DS, Meyer FG (2006) Nonlinear classification of EEG data for seizure detection. In: 3rd IEEE International Symposium on Biomedical Imaging. pp. 956-959.
35. Graichen U, Eichardt R, Fiedler P, Strohmeier D, Haueisen J (2011) Adaptive spatial harmonic analysis of eeg data using laplacian eigenspace. In: Noninvasive Functional Source Imaging of the Brain and Heart 2011 8th International Conference on Bioelectromagnetism (NFSI & ICBEM) 2011, 8th International Symposium on. pp. 18-21.
36. Chavel I (1984) Eigenvalues in Riemannian Geometry, volume 115 of Pure and Applied Mathematics. Academic Press.
37. Rosenberg S (1997) The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds. Number 31 in London Mathematical Society Student Texts. Cambridge University Press.
38. Wardetzky M, Mathur S, Kälberer F, Grinspun E (2007) Discrete laplace operators: No free lunch. In: Belyaev A, Garland M, editors, SGP07: Eurographics Symposium on Geometry Processing. Eurographics Association, pp. 33-37.
39. Berger M (2003) A Panoramic View of Riemannian Geometry. Springer.
40. Taubin G (1995) Signal processing approach to fair surface design. In: Proceedings of the ACM SIGGRAPH Conference on Computer Graphics. pp. 351-358.
41. Sorkine O (2006) Differential representations for mesh processing. Computer Graphics Forum 25: 789-807. doi: 10.1111/j.1467-8659.2006.00999.x
42. Zhang H, van Kaick O, Dyer R (2010) Spectral mesh processing. Computer Graphics Forum 29: 1865-1894. doi: 10.1111/j.1467-8659.2010.01655.x
43. Fujiwara K (1995) Eigenvalues of Laplacians on a closed riemannian manifold and its nets. Proceedings of the American Mathematical Society 123: 2585-2594. doi: 10.1090/S0002-9939-1995-1257106-5
44. Pinkall U, Polthier K (1993) Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2: 15-36. doi: 10.1080/10586458.1993.10504266
45. Polthier K (2002) Computational aspects of discrete minimal surfaces. In: Hass J, Hoffman D, Jaffe A, Rosenberg H, Schoen R, Wolf M, editors, Proceedings of the Clay Summer School on Global Theory of Minimal Surfaces.
46. Meyer M, Desbrun M, Schröder P, Barr A (2003) Discrete differential geometry operators for triangulated 2-manifolds. In: Hege HC, Polthier K, editors, Visualization and Mathematics III, Springer. pp. 35-57.
47. Dyer R, Zhang RH, Möller T, Clements A (2007) An investigation of the spectral robustness of mesh laplacians. Technical report, Simon Fraser University, GrUVi Lab, Burnaby, Canada.
48. Vallet B, Levy B (2007) Spectral geometry processing with manifold harmonics. Technical Report inria-00186931, Université Nancy, Institut National Polytechnique de Lorraine.
49. Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, et al. (1999) LAPACK Users' Guide. Society for Industrial and Applied Mathematics, 3rd edition.
50. Golub GH, Van Loan CF (1996) Matrix Computations. Johns Hopkins University Press, 3rd edition.
51. Dhillon IS, Parlett BN (2004) Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices. Linear Algebra and its Applications 387: 1-28. doi: 10.1016/j.laa.2003.12.028
52. Neymeyr K (2003) Solving mesh eigenproblems with multigrid efficiency. In: Kuznetsov Y, Neittaanmäki P, Pironneau O, editors, Numerical Methods for Scientific Computing. Variational problems and applications. CIMNE, Barcelona.
53. Mauguiere F, Allison T, Babiloni C, Buchner H, Eisen AA, Goodin DS, et al. (1999) Somatosensory evoked potentials. In: Deuschl G, Eisen A, editors, Recommendations for the Practice of Clinical Neurophysiology: Guidelines of the International Federation of Clinical Neurophysiology, Elsevier Science B. V., chapter 2.4. pp. 79-90.
54. Cruccu G, Aminoff M, Curio G, Guerit J, Kakigi R, Mauguiere F, et al. (2008) Recommendations for the clinical use of somatosensory-evoked potentials. Clinical Neurophysiology 119: 1705-1719. doi: 10.1016/j.clinph.2008.03.016 PMID: 18486546