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Preface
Author(s) -
Rhodes Arthur R.
Publication year - 2005
Publication title -
dermatologic therapy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.595
H-Index - 68
eISSN - 1529-8019
pISSN - 1396-0296
DOI - 10.1111/j.1529-8019.2005.00043.x
Subject(s) - medicine , dermatology
Since their introduction in the pioneering work by Schoenberg [73], splines have become one of the powerful tools in mathematics [2, 44, 74, 75, 94] and, for example, in computer-aided geometric designs [20, 27, 43, 45, 56, 103]. In recent decades, splines have served as a source for the wavelet [1, 3, 4, 10, 12, 15, 29, 37, 38, 57, 68, 78, 87, 90, 91, 95, 100, 101, 102], multiwavelet [11, 41, 72, 80], and wavelet frame constructions [14, 17, 19, 35, 36, 42, 64, 69]. Splines and splinebased wavelets, wavelet packets, and frames have been extensively used in signal and image processing applications [5, 6, 9, 13, 16, 22, 24, 25, 31, 32, 46, 49, 51, 52, 63, 79, 84, 86, 88, 89], to name a few. An excellent survey for the state-of-the-art (as of year 1999) on spline theory and applications is given in [85]. This survey motivated us in writing the present book. Another motivation was the emergence in recent years of new contributions of splines to wavelet analysis and its applications. In addition, we believe that the so-called discrete splines and their applications deserve a systematic exposure. Discrete splines [30, 50, 58, 59, 60, 61, 65, 75, 92], whose properties mimic the properties of polynomial splines, are the discrete-time counterparts of polynomial splines. They provide natural tools for handling discrete-time signal processing problems and serve as a source for the design of wavelet transforms [7, 8, 54, 66] and frames transforms [14, 18, 105], whose properties perfectly fit signal/image processing applications. The goal of this book is to provide a universal toolbox accompanied by a MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets, and wavelet frames for signal/image processing applications. The book is divided into two volumes. In Volume I ([26]), periodic splines and their diverse signal processing applications are discussed. The current Volume II deals with non-periodic splines. In this book, known and new contributions of splines to signal and image processing are described from a unified perspective, which is based on the Zak transform (ZT) [28, 93]. Being applied to B-splines, the ZT produces sets of so-called exponential splines (in Schoenberg [74]