Nonlinear Smoothing and Multiresolution Analysis

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.