Spline and Spline Wavelet Methods with Applications to Signal and Image Processing

This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discreteand 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 designof 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 performfast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and imagesup sampling. In addition tothe design of a diverse library of splines, SW, SWP and SWF, this book describes their applications topractical problems. The applications include up sampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SW Fare utilized for image restoration that was degraded by noise, blurring and loss of significant number of pixels. The bookis accompanied by Matlab based software that demonstrates and implements all the presented algorithms. The book combines extensive theoretical exposurewith detailed description of algorithms, applications and software. The Matlab software can be downloaded from http://extras.springer.com

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