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 polynomialperiodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based onZak transform and onSpline Harmonic Analysis (SHA) methodology.SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fouriertransform. 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, producedby waveletsdesign process, give birth tosubdivision 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 theirapplications topractical problems. The applications include up sampling, image denoising,recovery from blurred images, hydro-acoustic target detection, to name a few. TheSWFare utilized for imagerestoration that was degraded by noise, blurring and loss of significant number of pixels. The bookis accompanied byMatlab based software that demonstrates andimplements 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.