This volume provides universal methodologies accompanied by Matlab
software to manipulate numerous signal and image processing
applications. It is done with discrete and polynomial periodic splines.
Various contributions of splines to signal and image processing from a
unified perspective are presented. This presentation is based on Zak
transform and on Spline Harmonic Analysis (SHA) methodology. SHA
combines approximation capabilities of splines with the computational
efficiency of the Fast Fourier transform. SHA reduces the design of
different spline types such as splines, spline wavelets (SW), wavelet
frames (SWF) and wavelet packets (SWP) and their manipulations by simple
operations. Digital filters, produced by wavelets design process, give
birth to subdivision schemes. Subdivision schemes enable to perform fast
explicit computation of splines' values at dyadic and triadic rational
points. This is used for signals and images up sampling. In addition to
the design of a diverse library of splines, SW, SWP and SWF, this book
describes their applications to practical problems. The applications
include up sampling, image denoising, recovery from blurred images,
hydro-acoustic target detection, to name a few. The SWF are utilized for
image restoration that was degraded by noise, blurring and loss of
significant number of pixels. The book is accompanied by Matlab based
software that demonstrates and implements all the presented algorithms.
The book combines extensive theoretical exposure with detailed
description of algorithms, applications and software.
The Matlab software can be downloaded from http: //extras.springer.com
