Titre : | Noise reduction by wavelet thresholding | Type de document : | texte imprimé | Auteurs : | Maarten JANSEN, Auteur | Editeur : | Springer Verlag | Année de publication : | Cop. 2001 | Collection : | Lecture notes in statistics num. 161 | Importance : | XIX-191 p. | ISBN/ISSN/EAN : | 978-0-387-95244-4 | Langues : | Anglais | Mots-clés : | ondelette contrôle automatique bruit électronique méthode statistique technique digitale | Résumé : | This book discusses statistical applications of wavelet theory for use in signal and image processing. The emphasis is on smoothing by wavelet thresholding and extended methods. Wavelet thresholding is an example of non-linear and non-parametric smoothing. The first part discusses theoretical and practical issues concerned with minimum risk thresholding and fast threshold estimation, using generalized cross validation.
The extensions in later chapters consider possibilities to exploit three key properties of wavelets in statistics: sparsity, multiresolution, and locality. The author discusses original contributions to problems of correlated noise, scale dependent processing, Bayesian algorithms with geometrical priors (Markov random fields), non-equispaced data, and many other extensions.
The point of view lies on the bridge between statistics, signal and image processing, and approximation theory, and the book is accessible for researchers from all of these fields. Most of the material has in mind applications in signal or image processing, and signals and images are used extensively in the illustrations. Nevertheless, the algorithms are quite general in the sense that they could also serve in other regression problems. The book also pays attention to fast algorithms, and Matlab code reproducing many of the illustrations is available for free. | Note de contenu : | index, bibliogr. |
Noise reduction by wavelet thresholding [texte imprimé] / Maarten JANSEN, Auteur . - [S.l.] : Springer Verlag, Cop. 2001 . - XIX-191 p.. - ( Lecture notes in statistics; 161) . ISBN : 978-0-387-95244-4 Langues : Anglais Mots-clés : | ondelette contrôle automatique bruit électronique méthode statistique technique digitale | Résumé : | This book discusses statistical applications of wavelet theory for use in signal and image processing. The emphasis is on smoothing by wavelet thresholding and extended methods. Wavelet thresholding is an example of non-linear and non-parametric smoothing. The first part discusses theoretical and practical issues concerned with minimum risk thresholding and fast threshold estimation, using generalized cross validation.
The extensions in later chapters consider possibilities to exploit three key properties of wavelets in statistics: sparsity, multiresolution, and locality. The author discusses original contributions to problems of correlated noise, scale dependent processing, Bayesian algorithms with geometrical priors (Markov random fields), non-equispaced data, and many other extensions.
The point of view lies on the bridge between statistics, signal and image processing, and approximation theory, and the book is accessible for researchers from all of these fields. Most of the material has in mind applications in signal or image processing, and signals and images are used extensively in the illustrations. Nevertheless, the algorithms are quite general in the sense that they could also serve in other regression problems. The book also pays attention to fast algorithms, and Matlab code reproducing many of the illustrations is available for free. | Note de contenu : | index, bibliogr. |
| ![Noise reduction by wavelet thresholding vignette](https://math22.math.univ-montp2.fr/images/vide.png) |