Analyse de signaux et d'images par bancs de filtres : applications aux géosciences

Abstract : Our main purpose in this PhD thesis is to perform local frequential (or directional) processing in different kind of data (volumes, images or signals). To this end, filter banks (FBs) are studied. More precisely, we first investigate the existence and the construction of synthesis FBs inverse to a given FIR complex analysis FB. Through the study of the polyphase analysis matrix, we are able to propose methods to test the invertibility and to build one inverse FB. Using this inverse, we provide a parametrization of the set of synthesis FB, with which we optimize filter responses with different criteria. The same study is performed in the multidimensional case. Since FBs provide an efficient representation of structured information in data, it is then possible to preserve them while rejecting unwanted perturbations. By associating Stein's principle and those FB, we proposed two methods to denoise signals and images corrupted by Gaussian noise. These methods, named FB-SURELET-E and FB-SURELET-C, are compared to recent denoising methods and are found to offer good results, especially for textured images. Another type of application is then investigated : separation of oriented structures. To this end, we have developed an anisotropic filtering method. The different proposed methods are finally applied on images and signals from various fields : seismic images and cubes, transmission electron microscopy (TEM) images of catalysts and vibration signals from car engines
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Theses
Engineering Sciences [physics]. Université Paris-Est, 2008. French


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Jérôme Gauthier. Analyse de signaux et d'images par bancs de filtres : applications aux géosciences. Engineering Sciences [physics]. Université Paris-Est, 2008. French. <tel-00331238v2>

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