Nonlinear smoothing and multiresolution analysis
By: Carl Rohwer.
Series: International series of numerical mathematics -- v. 150.
Publisher: Birkhäuser Verlag
Published: 2005
Place of publication: Basel; Boston
Language: eng
Number of pages: 137
Subjects: Nonlinear theories; Fourier analysis; Mathematics -- Computer simulation
Description: 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.
Notes: Includes bibliographical references  (p. [131]-133) and index.