Source localization in ellipsoids by the best meromorphic approximation in planar sections

Inverse Problems

Volumn 24, Issue 3, 2008, Pages

  Leblond, Juliette ^a   Paduret, Cristina ^b   Rigat, Stéphane ^a,b   Zghal, Meriem ^a,c  

^a INRIA   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

^c ENIT LAMSIN   (Tunisia)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; ELECTROENCEPHALOGRAPHY; HARMONIC ANALYSIS; LARGE SCALE SYSTEMS;

COMPLEX ANALYSIS; MEROMORPHIC APPROXIMATION; SINGULARITIES; SOURCE LOCALIZATION;

INVERSE PROBLEMS;

EID: 44449126119     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/24/3/035017     Document Type: Article

References (45)

1. Adamyan V M, Arov D Z and Krein M G 1971 Analytic properties of Schmidt pairs, Hankel operators, and the generalized Schur-Takagi problem Mat. Sb. 128 34-75
2. Adamyan V M, Arov D Z and Krein M G 1971 Analytic properties of Schmidt pairs, Hankel operators, and the generalized Schur-Takagi problem Math. USRR Sb. 15 (Engl. transl.)
3. Axler S, Bourdon P and Ramey W 2001 Harmonic Function Theory 2nd edn GTM (Berlin: Springer)
4. 2-approximants of linear systems IMA J. Math. Control Inform. 3 89-101
5. Baratchart L, Ben Abda A, Ben Hassen F and Leblond J 2005 Recovery of pointwise sources or small inclusions in 2D domains and rational approximation Inverse Problems 21 51-74
6. Baratchart L, Leblond J and Marmorat J-P 2006 Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices Electron. Trans. Numer. Anal. 25 41-53
7. 2 Theor. Comput. Sci. 94 175-97
8. 2 rational approximation J. Anal. Math. 70 225-66
9. Baratchart L and Stahl H Asymptotic spectrum of Hankel operator with branched symbol (in preparation)
10. p analog to AAK theory for p ≥ 2 J. Funct. Anal. 191 52-122
11. 2 of the circle Constr. Approx. 17 103-38
12. Baratchart L and Yattselev M Meromorphic and multipoint Padé approximants for complex Cauchy transforms with polar singularities Preprint
13. Baratchart L and Yattselev M Strong asymptotics for non-Hermitian orthogonal polynomials and Blaschke products on a segment (submitted)
14. Ben Hassen F, Leblond J, Rigat S and Zghal M EEG inverse problems in ellipsoid by data approximation on the boundary (in preparation)
15. Byerly E 1893 Fourier's Series (New York: Dover)
16. Byerly E 1959 Fourier's Series (New York: Dover (second reprint))
17. Chafik M, El Badia A and Ha-Duong T 2000 On some inverse EEG problems Inverse Problems in Engineering Mechanics vol II pp 537-44
18. Dassios G and Kariotou F 2003 Magnetoencephalography in ellipsoidal geometry J. Math. Phys. 44 220-41
19. Dassios G and Kleinman R 2000 Low frequency scattering Oxford Science Publications: The Clarendon Press (New York: Oxford University Press) 297 pp
20. Dautray R and Lions J-L 1987 Analyse Mathématique et Calcul Numérique vol 2 (Paris: Masson)
21. Ebenfelt P, Khavinson D and Shapiro H S 2001 An inverse problem for the double layer potential Comput. Methods Funct. Theory 1 387-402
22. El Badia A and Ha-Duong T 2000 An inverse source problem in potential analysis Inverse Problems 16 651-63
23. Faugeras O et al 1999 The inverse EEG and MEG problems: the adjoint state approach: I. The continuous case INRIA Research Report no. 3673
24. Hämäläinen M, Hari R, Ilmoniemi J, Knuutila J and Lounasmaa O V 1993 Magnetoencephalography theory, instrumentation and applications to noninvasive studies of the working human brain Rev. Mod. Phys. 65 413-97
25. Hobson E W 1931 Spherical and Ellipsoidal Harmonics (Cambridge: Cambridge University Press)
26. Hobson E W 1965 Spherical and Ellipsoidal Harmonics (Cambridge: Cambridge University Press) (second reprint)
27. Hofmann-Wellenhof B and Moritz H 2005 Physical Geodesy (New York: Springer)
28. Holota P 2003 On the computation of ellipsoidal harmonics in potential problems of geodetic relevance Geophys. Res. Abstr. 5
29. Holota P 2004 An approximation of ellipsoidal harmonics in refined studies on earth gravitational potential EGU, 1st General Assembly, Nice, France, 25-30 April 2004
30. Irimia A 2005 Electric field and potential calculation for a bioelectric current dipole in an ellipsoid J. Phys. A: Math. Gen. 38 8123-38
31. Isakov V 1990 Inverse source problems Mathematical Surveys and Monographs vol 34 (Providence, RI: American Mathematical Society)
32. Kariotou F 2004 Electroencephalography in ellipsoidal geometry J. Math. Anal. Appl. 290 324-42
33. Leblond J, Paduret C, Rigat S and Zghal M 2008 Source localization in ellipsoids by best meromorphic approximation in planar sections (unpublished) http://www-sop.inria.fr/apics/personnel/ Juliette.Leblond/publications.html
34. Marmorat J-P and Olivi M 2007 Nudelman interpolation, parametrization of lossless functions and balanced realizations Automatica 43 1329-38
35. 2 approximation: a state-space approach using Schur parameters Proc. CDC-IEEE'02, Las-Vegas
36. Nara T and Ando S 2003 A projective method for an inverse source problem of the Poisson equation Inverse Problems 19 355-69
37. Nara T 2008 An algebraic method for identification of dipoles and quadrupoles Inverse Problems 24 at press
38. Nikolski N K 2002 Operator, functions, and systems: an easy reading Hardy, Hankel, and Toeplitz vol 1 (Mathematical Surveys and Monographs) (Providence, RI: American Mathematical Society) p 92
39. Peller V V 2003 Hankel Operators and their Applications (Berlin: Springer)
40. Stahl H 1985 The structure of extremal domains associated with an analytic function Complex Var. Theory Appl. 4 339-54
41. Sten J C-E 2006 Ellipsoidal harmonics and their applications in electrostatics J. Electrost. 64 647-54
42. Sudbery A 1979 Quaternionic analysis Math. Proc. Camb. Phil. Soc. 85 199-225
43. Vessella S 1992 Locations and strengths of point sources: stability estimates Inverse Problems 8 911-7
44. Whittaker T and Watson G N 1963 A Course of Modern Analysis (Cambridge: Cambridge University Press)
45. Young N J 1998 Introduction to Hilbert Space (Cambridge: Cambridge University Press)