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Analyse spectrale à haute résolution de signaux irrégulièrement échantillonnés : application à l'Astrophysique.

Abstract : The study of many astrophysical phenomena is based on the search for periodicities from time series, as light or radial velocity curves.
Because of observation constraints, astrophysical data generally suffer missing data and irregular sampling. Thus, Fourier-based spectral analysis may not be satisfactory, and widespread heuristic CLEAN deconvolution methods may lack accuracy.
This thesis addresses spectral analysis as an inverse problem, where the spectrum is discretized on an arbitrarily thin frequency grid. Regularization is then addressed by taking into account the prior sparseness of the solution, as we focus on line spectra estimation.
A first approach considers the minimization of a penalized least-squares criterion, where the penalization function is designed to retrieve sparse solutions. In particular, penalization by the l1-norm is studied in application to complex variables, that shows a satisfactory behavior in terms of prior modeling. Several powerful optimization algorithms are developed that allow a very high spectral resolution.
Second, a probabilistic regularization is studied by modeling the spectral amplitudes as the realization of a Bernoulli-Gaussian process. Bayesian posterior mean estimation is then addressed using Monte-Carlo Markov Chain methods, which enable a fully unsupervised procedure. The probabilistic interpretation of the estimator combined with variance information for each estimated parameter then provides confidence levels, which is crucial information for astronomy. Significant algorithmic improvements are proposed to accelerate the classic Gibbs sampling algorithm. Then, continuous-valued frequency shifts are introduced that substantially improve the frequency precision at a reasonable computational cost.
Simulations illustrate the estimation quality for each method and the performances of the proposed algorithms. An application to astrophysical experimental data is finally presented that brings out the advantage of this methodology compared to classic spectral analysis methods.
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Contributor : Sébastien Bourguignon Connect in order to contact the contributor
Submitted on : Tuesday, November 28, 2006 - 11:36:45 AM
Last modification on : Tuesday, October 19, 2021 - 6:57:14 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:33:47 PM


  • HAL Id : tel-00116827, version 1



Sébastien Bourguignon. Analyse spectrale à haute résolution de signaux irrégulièrement échantillonnés : application à l'Astrophysique.. Traitement du signal et de l'image [eess.SP]. Université Paul Sabatier - Toulouse III, 2006. Français. ⟨tel-00116827⟩



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