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MÉTHODES MARKOVIENNES EN ESTIMATION SPECTRALE NON PARAMETRIQUES. APPLICATION EN IMAGERIE RADAR DOPPLER

Abstract : We address the problem of spectral analysis from a small number of data. Casted into a Fourier synthesis framework, short time spectral analysis is an underdetermined linear inverse problem. Regularization by penalization is an appealing approach to incorporate prior information on the sought spectrum, where a penalization function is combined with a data-based term in a regularized criterion. The spectral estimate is defined as the global minimizer of the criterion. The penalization function is specifically designed in three studied cases: the restoration of line, smooth and mixed spectra. Mixed spectra correspond to situations where peaks are embedded in smooth spectral components. The stress is put on the construction of convex penalization functions because they ensure the well-posedness of the regularized problem and they simplify the computation of the solution. Furthermore, we recommend to use circular functions, i.e. depending only on the magnitude of the sought Fourier coefficients. In addition, separable, Markovian and compound functions are retained to retrieve lines, smooth and mixed spectra, respectively. Choosing a convex function for smooth and mixed spectra restoration happens to lead to non derivable criteria. Consequently, we use a Graduated Nondifferentiability approach to compute the estimate. From an algorithmic point of view, the IRLS algorithm reveals the most efficient technique but is only available for line spectra estimation. We develop generalizations for the other cases, based on the half-quadratic development of the penalization function. The resulting block-coordinate descent method is converging and competitive with a pseudo-conjugate gradient algorithm. Finally, processing examples fully demonstrate the validity of the new approach, in the field of Doppler radar imaging from synthetic as well as real measures.
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https://tel.archives-ouvertes.fr/tel-00003664
Contributor : Philippe Ciuciu <>
Submitted on : Thursday, October 30, 2003 - 5:29:50 PM
Last modification on : Wednesday, September 16, 2020 - 4:42:26 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 11:15:10 AM

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Philippe Ciuciu. MÉTHODES MARKOVIENNES EN ESTIMATION SPECTRALE NON PARAMETRIQUES. APPLICATION EN IMAGERIE RADAR DOPPLER. Autre. Université Paris Sud - Paris XI, 2000. Français. ⟨tel-00003664⟩

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