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Méthodes numériques temps-échelle et temps-fréquence pour le traitement du signal et des images

Abstract : This thesis examines various methods of Time-Scale and Time-Frequency analysis. The aim is to adapt existing numerical algorithms and to conceive new techniques allowing to transform a signal or an image into the most appropriate representation in space. This decomposition can then be used to solve certain problems of denoising, segmentation, compression, analysis or classification. The various aspects examined in the thesis can be divided up into four main areas: - Undecimated wavelet transform. Undecimated methods of denoising are used and extended to the iterative treatment of a sequence of acquisitions bearing on the same signals. - Wavelet maxima. Starting from this representation, a method of image denoising is suggested, using the evolution of the angles of derivatives across the scales. We then suggest an algorithm of signal partition based on a new method of maxima chaining. / This leads to the suggestion of an algorithm... - Malvar's wavelets. A fast algorithm of non-dyadic decomposition into Malvar's wavelets is introduced, as well as a cost function based on spectral distances, generalized to dimension 2 by way of anisotropic decomposition. - Meyer's wavelets. This decomposition is achieved by frequential windowing procedure. We introduce an algorithm of discrete decomposition-reconstruction into Meyer's wavelet packets, followed by a definition of non-uniform wavelet packet decomposition. Finally, using the double-tree principle, decomposition is defined as being non-uniform in both the temporal and frequential planes.
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Contributor : Philippe Carré <>
Submitted on : Monday, June 13, 2005 - 3:17:48 PM
Last modification on : Wednesday, September 5, 2018 - 1:30:05 PM
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  • HAL Id : tel-00009451, version 1



Philippe Carré. Méthodes numériques temps-échelle et temps-fréquence pour le traitement du signal et des images. Traitement du signal et de l'image [eess.SP]. Université de Poitiers, 2000. Français. ⟨tel-00009451⟩



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