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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
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