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

Beschreibung

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 upsampling. 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 upsampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SWF are utilized for image restoration that were degraded by noise, blurring and loss of significant number of pixels. The book is accompanied by a 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
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
Provides a universal toolbox accompanied by Matlab software Can be used as supplementary reading Presents a new generic approach to the wavelets and frames design Includes supplementary material: sn.pub/extras

Autor*in

Amir Z. Averbuch

Themen in »Spline and Spline Wavelet Methods with Applications to Signal and Image Processing«

Frames Images Signals Splines Wavelets

Stimmen zu »Spline and Spline Wavelet Methods with Applications to Signal and Image Processing«

“The purpose of this book is to thoroughly prepare the reader for a research in spline and spline wavelet methods to signal and image processing theory at an advance level. … The book is a textbook for graduate students and one of the major consulting reference for the researcher in the field of spline wavelet theory and image processing.” (Haydar Akca, zbMATH 1316.65019, 2015)

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