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＜電子ブック＞
Nonlinear Smoothing and Multiresolution Analysis / by Carl Rohwer
(International Series of Numerical Mathematics. ISSN:22966072 ; 150)

版	1st ed. 2005.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2005
本文言語	英語
大きさ	XIV, 137 p : online resource
著者標目	*Rohwer, Carl author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Approximation theory LCSH:Fourier analysis LCSH:Operator theory LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Signal processing FREE:Mathematics FREE:Approximations and Expansions FREE:Fourier Analysis FREE:Operator Theory FREE:Mathematical and Computational Engineering Applications FREE:Signal, Speech and Image Processing
一般注記	Operators on Sequences -- Basic Rank Selectors, Pulses and Impulses -- LULU-Smoothers, Signals and Ambiguity -- LULU-Intervals, Noise and Co-idempotence -- Smoothing and Approximation with Signals -- Variation Reduction and Shape Preservation -- Multiresolution Analysis of Sequences -- The Discrete Pulse Transform -- Fair Comparison with Linear Smoothers -- Interpretation and Future 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 HTTP:URL=https://doi.org/10.1007/3-7643-7382-2

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