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Nonlinear Smoothing and Multiresolution Analysis

By: Rohwer, Carl [author.].
Contributor(s): SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: International Series of Numerical Mathematics ; 1500.Publisher: Basel : Birkh�user Basel, 2005. Description: XIV, 137 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764373825.Subject(s): Mathematics | Approximation theory | Fourier analysis | Operator theory | Applied mathematics | Engineering mathematics.1 | Mathematics.2 | Mathematics, general.2 | Approximations and Expansions.2 | Fourier Analysis.2 | Operator Theory.2 | Appl.Mathematics/Computational Methods of Engineering.2 | Signal, Image and Speech Processing.2DDC classification: 510 Online resources: Click here to access online
Contents:
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.
In: Springer eBooks0Summary: 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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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK6491
Total holds: 0

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.

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