Nonlinear smoothing and multiresolution analysis
著者
書誌事項
Nonlinear smoothing and multiresolution analysis
（International series of numerical mathematics, v. 150）
Birkhäuser, c2005
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注記
Includes bibliographical references (p. [131]-133) and index
内容説明・目次
内容説明
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.
目次
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.
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