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Nonlinear Smoothing and Multiresolution Analysis

  • Carl Rohwer
Book

Part of the International Series of Numerical Mathematics book series (ISNM, volume 150)

About this book

Introduction

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.

Keywords

Analysis Fourier analysis Mathematical morphology Multiresolution analysis Numerical analysis Signal Signal processing Wavelet image processing operator simulation

Authors and affiliations

  • Carl Rohwer
    • 1
  1. 1.Department of MathematicsUniversity of StellenboschSouth Africa

Bibliographic information