Noise reduction by wavelet thresholding

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Wavelet methods are increasingly used in signal and image processing, with this text focusing on statistical applications, particularly wavelet-based smoothing. It presents examples of non-linear and non-parametric curve fitting, aiming to bridge the gap between statisticians and application-oriented fields, including signals and images. While it analyzes existing methods, the book does not seek to provide a comprehensive overview, as that would introduce bias towards the author's algorithms. Instead, it introduces new material and insights related to wavelet-based noise reduction while covering a range of methodologies, making it a useful introduction to wavelet smoothing. Key properties such as sparsity, locality, and multiresolution are emphasized throughout, as most wavelet methods leverage at least one of these aspects. The research presented is part of the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State's Prime Minister's Office for Science, Technology, and Culture. The author assumes scientific responsibility, with research funded by a grant from the Flemish Institute for the Promotion of Scientific and Technological Research in the Industry (IWT) from 1995 to 1999.