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Caractérisation des images stationnaires par des modèles non gaussiens bidimensionnels à moyenne ajustée

Characterization of stationary images by non gaussian bidimensional moving average models

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Résumé

Dans cet article on développe quatre méthodes linéaires des moindres carrés consacrées à ľidentification des signaux non gaussiens bidimensionnels (2-D) à moyenne ajustée (ma), éventuellement à phase non minimale (pnm), ainsi qu’une relation liant ľautocorrélation et les cumulants. Ľune des méthodes est fondée uniquement sur les cumulants tandis que les autres exploitent à la fois les autocorrélations et les cumulants ďordre m (m > 2). Ces méthodes sont non surparamétrisées et non restreintes aux cas où les deux coefficients extrêmes b(qp q2) et b(0,0) du modèle ma, ďordre (q1, q2), sont non nuls. La relation présentée et trois méthodes parmi les quatre proposées dérivent de la transformation de ľéquation non linéaire de Brillinger et Rosenblatt en relations linéaires grâce à la solution explicite de Tugnait (formule modifiée de la version 2-D de ľalgorithme ‘C(q, k)’ de Giannakis). Une généralisation à ľordre m de la version 2-D de la méthode classique de Giannakis-Mendel est aussi présentée. Et par des simulations sur deux tailles du même signal ma 2-D synthétique, en ľabsence et en présence de bruit, on évalue les performances des méthodes développées et de la solution explicite de Tugnait en les comparant, puis on teste la relation proposée sous un environnement bruité, et on termine par une application à la caractérisation ďune image réelle homogène texturée par un modèle ma 2-D que nous identifierons dans le cas bruité et non bruité.

Abstract

In this paper, four batch least squares linear approaches are presented for identification of non minimum phase bidimensional non Gaussian moving average (MA) models, and a relationship between autocorrelation and cumulant sequences is given. One of the proposed methods is cumulant-based only but the others use both autocorrelations and m-th order cumulants (m. > 2). Three of them are derived from the Brillinger-Rosenblatt’s non linear relation by using the Tugnait’s closed-form solution. Also, we generalize to m-th order cumulants the 2-D version of Giannakis-Mende’s approach. By simulations, we test and compare the Tugnait’s closed-form solution and the proposed methods, and we evaluate the performance of our relationship in noisy environment. Finally, we propose to characterize textured images by a 2-D ma model witch will be identified using our approaches in noisy and free noise cases.

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Correspondence to M’hamed Bakrim or Driss ABoutajdine.

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Bakrim, M., ABoutajdine, D. Caractérisation des images stationnaires par des modèles non gaussiens bidimensionnels à moyenne ajustée. Ann. Télécommun. 56, 523–537 (2001). https://doi.org/10.1007/BF03008830

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