']; end; end; Ker4=Ker; display('* Fin des calculs ,
Ker1 Ker2 Ker3 Ker4; display('* Donnees sauvegardees dans le fichier KERN ,
* Modifications des noyaux *') for ii=1:L W2(ii)=W2(ii)*sin, p.21 ,
for i=1:N1 Lig=[zeros(N2*(i-1),1);W4';zeros ,
* linear search of tau *') ko=0; while ko<NUM ko=ko+1; fnum=factk/NUM, factk+(NUM-ko)*fnum ,
W2'; II=[]; for compj=1:length(V) II=[II,wdf]; end, WWW=Ker.*(II' ,
'-s)^2; alpha=(wdf'*Matr)*W2'; flnf=wdf, *(log ,
Ker1 Ker2 Ker3 Ker4; save ,
Maximum entropy regularization of Fredholm integral equations of the first kind, Inverse Problems, vol.7, issue.6, pp.739-808, 1991. ,
DOI : 10.1088/0266-5611/7/6/004
A comparative study of three techniques for using the spectral matrix in wave analysis, Radio Science, vol.34, issue.10, pp.833-845, 1976. ,
DOI : 10.1029/RS011i010p00833
Lp approximation of variational problems in L1 and L???, Nonlinear Analysis: Theory, Methods & Applications, vol.36, issue.3, pp.373-399, 1999. ,
DOI : 10.1016/S0362-546X(98)00078-9
Eléments d'analyse convexe et variationnelle, ellipses, 1997. ,
Analysis and control of nonlinear infinite dimensional systems, 1993. ,
Duality Relationships for Entropy-Like Minimization Problems, SIAM Journal on Control and Optimization, vol.29, issue.2, pp.325-338, 1991. ,
DOI : 10.1137/0329017
Convergence of Best Entropy Estimates, SIAM Journal on Optimization, vol.1, issue.2, pp.191-205, 1991. ,
DOI : 10.1137/0801014
Partially-Finite Programming in $L_1 $ and the Existence of Maximum Entropy Estimates, SIAM Journal on Optimization, vol.3, issue.2, pp.248-267, 1993. ,
DOI : 10.1137/0803012
Maximum Entropy Reconstruction Using Derivative Information, Part 1: Fisher Information and Convex Duality, Mathematics of Operations Research, vol.21, issue.2, pp.442-468, 1996. ,
DOI : 10.1287/moor.21.2.442
Analyse fonctionnelle, 1999. ,
One and two direction models for VLF electromagnetic waves observed on-board Geos 1, Journal of Geophysical Research, vol.15, issue.A4, pp.2377-2383, 1981. ,
DOI : 10.1029/JA086iA04p02377
Maximum entropy in action, 1991. ,
IntroductionàIntroductionà l'analyse numérique matricielle etàetà l'optimisation, Dunod, 1998. ,
Convergence Rates for Maximum Entropy Regularization, SIAM Journal on Numerical Analysis, vol.30, issue.5, pp.1509-1536, 1993. ,
DOI : 10.1137/0730079
Elliptic partial differential equation of the second order, 2001. ,
Introduction to numerical analysis, 1956. ,
The Freja wave and plasma density experiment, Space Science Reviews, vol.70, issue.3-4, pp.577-592, 1994. ,
DOI : 10.1007/BF00756887
The analysis of linear partial differential operators I, 1990. ,
An introduction to the mathematical theory of inverse problems, 1996. ,
Regularization of nonlinear illposed problems with closed operators, Numerical Functional Analysis and Optimization, vol.14, issue.3-4, pp.389-404, 1993. ,
DOI : 10.1016/0022-247X(80)90145-6
Analyse de champs d'ondesélectromagnétiquesondesélectromagnétiques aléatoires observées dans la ma-gnétosphèrè a partir de la mesure simultanée de leur six composantes, Thèse d'´ etat, 1977. ,
Analysis of random electromagnetic wave field by a maximum entropy method, Ann. Télécom, vol.34, pp.204-213, 1979. ,
On the use of the wave distribution function concept to determine the directions of arrivals of radar echoes, Planetary and Space Science, vol.48, issue.12-14, pp.1321-1328, 2000. ,
DOI : 10.1016/S0032-0633(00)00112-4
Determination of the wave-vector spectrum for plasma waves and turbulence observed in space plasmas, Journal of Atmospheric and Terrestrial Physics, vol.54, issue.10, pp.1227-1235, 1992. ,
DOI : 10.1016/0021-9169(92)90031-F
Wave distribution functions estimation of VLF electromagnetic waves observed onboard Geos 1, Journal of Geophysical Research, vol.10, issue.A4, pp.2359-2375, 1981. ,
DOI : 10.1029/JA086iA04p02359
A generalization of the maximal entropy method for solving ill-posed problems , Siberian Math, J, vol.41, pp.716-721, 2000. ,
Use of the three-dimensional covariance matrix in analyzing the polarization properties of plane waves, Journal of Geophysical Research, vol.75, issue.28, pp.5551-5559, 1972. ,
DOI : 10.1029/JA077i028p05551
The mathematics of computerized tomography, 1986. ,
Consistency of a nonlinear deconvolution method with applications to image restoration, Advances in Mathematical Sciences and Applications, vol.7, pp.798-808, 1997. ,
Digital signal processing [37] T. Oscarsson, Dual principles in maximum entropy reconstruction of the wave distribution function, J. Comput. Phys, pp.110-221, 1976. ,
Wave mode identification via wave distribution function analysis, Physics and Chemistry of the Earth, Part C: Solar, Terrestrial & Planetary Science, vol.26, issue.1-3, pp.229-235, 2001. ,
DOI : 10.1016/S1464-1917(00)00113-6
Statistical study of the propagation characteristics of ELF hiss observed on GEOS-1, inside and outside the plasmasphere, Ann. Geophys, vol.4, pp.363-384, 1986. ,
Interpretation of measurements of the polarization percentage for plasma waves, pp.82-95, 1992. ,
Numerical recipes, 1986. ,
Determination of a power density by an entropy regularization method, Journal of Applied Mathematics, vol.2005, issue.2, pp.127-152, 2005. ,
DOI : 10.1155/JAM.2005.127
URL : https://hal.archives-ouvertes.fr/hal-00022002
An entropy regularization method appplied to an ELF hiss event wave distribution function identification, (submited to, J. Geophys. Res.), vol.0, p.0, 2004. ,
Ill-posed problem solving by an entropy regularization method. application to the propagation analysis of electromagnetic waves, Proceedings of Contributed Papers : Part III -Physics (J. Safrankova Matfyzpress, pp.593-599, 2004. ,
Uber die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten, Ber. Ver. Sächs. Akad, vol.69, pp.262-277, 1917. ,
Convex analysis, 1970. ,
DOI : 10.1515/9781400873173
Local spectra and wave distribution functions, Journal of Geophysical Research, vol.40, issue.A3, pp.1809-1815, 1988. ,
DOI : 10.1029/JA093iA03p01809
Some comments on the descriptions of the polarisation states of waves, Geophys, J. R. Astron. Soc, pp.61-115, 1980. ,
Etude de la fonction de distribution des ondes dans un plasma chaud, Thèse, 1995. ,
Direct problem of the wave distribution function in a hot magnetospheric plasma, Proceeding of WDS 94, pp.19-23, 1994. ,
The wave distribution function in a hot magnetospheric plasma: The direct problem, Journal of Geophysical Research: Space Physics, vol.89, issue.A5, pp.10639-10651, 1996. ,
DOI : 10.1029/95JA03510
Application of wave distribution function methods to an ELF hiss event at high latitudes, Journal of Geophysical Research: Space Physics, vol.1, issue.16, pp.885-903, 2000. ,
DOI : 10.1029/2000JA900029
Théorie des distributions, Analyse IV -applicationsàapplicationsà la théorie de la mesure, 1966. ,
A mathematical theory of communication, The Bell System Technical, Journal, vol.27, pp.379-423623, 1948. ,
Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE Transactions on Information Theory, vol.26, issue.1, pp.26-36, 1980. ,
DOI : 10.1109/TIT.1980.1056144
Maximum-entropy and bayesian spectral analysis and estimations problems, 1987. ,
DOI : 10.1007/978-94-009-3961-5
Waves in plasmas, Am. Inst. of Phys, 1992. ,
Wave distribution function analysis of plasmaspheric hiss, 1987. ,
Theory for the interpretation of measurements of a random electromagnetic wave field in space, Space Res, vol.14, pp.381-386, 1974. ,
Numerical methods for the solution of ill-posed problems, 1995. ,
DOI : 10.1007/978-94-015-8480-7
Arsenin, Solutions of ill-posed problems, 1977. ,
The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Transactions on Audio and Electroacoustics, vol.15, issue.2, pp.70-73, 1967. ,
DOI : 10.1109/TAU.1967.1161901
Analyse harmonique réelle, 1995. ,
Functional analysis, 1980. ,
Nonlinear functional analysis and its applications, part I : Fixed point theorems, 1984. ,