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Nonlinear Smoothing and Multiresolution Analysis by Carl H. Rohwer

Carl H. Rohwer - Nonlinear Smoothing and Multiresolution Analysis
Publisher: Birkhäusеr Bаsel | 2005-07-01 | ISBN: 376437229X | PDF | 152 pages | 10.12 MB

This monograph presents a new theory for analysis, comparison and design of nonlinear smoothers, linking to established practices. Although a part of mathematical morphology, the special properties yield many simple, powerful and illuminating results leading to a novel nonlinear multiresolution analysis with pulses that may be as natural to vision as wavelet analysis is to acoustics. Similar to median transforms, they have the advantages of a supporting theory, computational simplicity, remarkable consistency, full trend preservation, and a Parceval-type identity. Although the perspective is new and unfamiliar to most, the reader can verify all the ideas and results with simple simulations on a computer at each stage. The framework developed turns out to be a part of mathematical morphology, but the additional specific structures and properties yield a heuristic understanding that is easy to absorb for practitioners in the fields like signal- and image processing. The book targets mathematicians, scientists and engineers with interest in concepts like trend, pulse, smoothness and resolution in sequences.









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