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Spline and Spline Wavelet Methods with Applications to Signal and Image Processing - Volume II: Non-Periodic Splines (Hardcover, 1st ed. 2016)
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Spline and Spline Wavelet Methods with Applications to Signal and Image Processing - Volume II: Non-Periodic Splines (Hardcover, 1st ed. 2016)
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This book presents various contributions of splines to signal and
image processing from a unified perspective that is based on the
Zak transform (ZT). It expands the methodology from periodic
splines, which were presented in the first volume, to non-periodic
splines. Together, these books provide a universal toolbox
accompanied by MATLAB software for manipulating polynomial and
discrete splines, spline-based wavelets, wavelet packets and
wavelet frames for signal/ image processing applications. In this
volume, we see that the ZT provides an integral representation of
discrete and polynomial splines, which, to some extent, is similar
to Fourier integral. The authors explore elements of spline theory
and design, and consider different types of polynomial and discrete
splines. They describe applications of spline-based wavelets to
data compression. These splines are useful for real-time signal
processing and, in particular, real-time wavelet and frame
transforms. Further topics addressed in this volume include:
"global" splines, such as interpolating, self-dual and smoothing,
whose supports are infinite; the compactly supported
quasi-interpolating and smoothing splines including
quasi-interpolating splines on non-uniform grids; and cubic Hermite
splines as a source for the design of multiwavelets and
multiwavelet frames. Readers from various disciplines including
engineering, computer science and mathematical information
technology will find the descriptions of algorithms, applications
and software in this book especially useful.
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