Nonlinear Smoothing and Multiresolution Analysis

This monograph presents a new theory for analysis, comparisonand design of nonlinear smoothers, linking to establishedpractices. Although a part of mathematical morphology, the specialproperties yield many simple, powerful and illuminating resultsleading to a novel nonlinear multiresolution analysis with pulsesthat may be as natural to vision as wavelet analysis is toacoustics. Similar to median transforms, they have the advantagesof a supporting theory, computational simplicity, remarkableconsistency, full trend preservation, and a Parceval-typeidentity.Although the perspective is new and unfamiliar to most, thereader can verify all the ideas and results with simple simulationson a computer at each stage. The framework developed turns out tobe a part of mathematical morphology, but the additional specificstructures and properties yield a heuristic understanding that iseasy to absorb for practitioners in the fields like signal- andimage processing.The book targets mathematicians, scientists and engineers withinterest in concepts like trend, pulse, smoothness and resolutionin sequences.