Spline and Spline Wavelet Methods with Applications to Signal and Image Processing: Volume II: Non-Periodic Splines

✍ Scribed by Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 441
• Edition: 1
• Category: Library

✦ Synopsis

This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications.

In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms.

Further topics addressed in this volume include: "global" splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames.

Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful.

✦ Table of Contents

Front Matter....Pages i-xxv
Introduction: Signals and Transforms ....Pages 1-8
Introduction: Digital Filters and Filter Banks....Pages 9-30
Mixed Convolutions and Zak Transforms....Pages 31-50
Non-periodic Polynomial Splines....Pages 51-85
Quasi-interpolating and Smoothing Local Splines....Pages 87-114
Cubic Local Splines on Non-uniform Grid....Pages 115-126
Splines Computation by Subdivision ....Pages 127-144
Polynomial Spline-Wavelets....Pages 145-169
Non-periodic Discrete Splines....Pages 171-188
Non-periodic Discrete-Spline Wavelets....Pages 189-214
Biorthogonal Wavelet Transforms....Pages 215-237
Biorthogonal Wavelet Transforms Originating from Splines....Pages 239-273
Data Compression Using Wavelet and Local Cosine Transforms....Pages 275-297
Wavelet Frames Generated by Perfect Reconstruction Filter Banks....Pages 299-361
Biorthogonal Multiwavelets Originated from Hermite Splines....Pages 363-392
Multiwavelet Frames Originated From Hermite Splines....Pages 393-407
Back Matter....Pages 409-426

✦ Subjects

Signal, Image and Speech Processing; Computer Imaging, Vision, Pattern Recognition and Graphics; Computational Mathematics and Numerical Analysis