Topic
Spline wavelet
About: Spline wavelet is a research topic. Over the lifetime, 263 publications have been published within this topic receiving 31392 citations.
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01 May 1992TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Abstract: Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal bases of wavelets and multiresolutional analysis Orthonormal bases of compactly supported wavelets More about the regularity of compactly supported wavelets Symmetry for compactly supported wavelet bases Characterization of functional spaces by means of wavelets Generalizations and tricks for orthonormal wavelet bases References Indexes.
16,073 citations
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
Abstract: We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.
8,588 citations
Book•
01 Jan 1992TL;DR: An Overview: From Fourier Analysis to Wavelet Analysis, Multiresolution Analysis, Splines, and Wavelets.
Abstract: An Overview: From Fourier Analysis to Wavelet Analysis. The Integral Wavelet Transform and Time-Frequency Analysis. Inversion Formulas and Duals. Classification of Wavelets. Multiresolution Analysis, Splines, and Wavelets. Wavelet Decompositions and Reconstructions. Fourier Analysis: Fourier and Inverse Fourier Transforms. Continuous-Time Convolution and the Delta Function. Fourier Transform of Square-Integrable Functions. Fourier Series. Basic Convergence Theory and Poisson's Summation Formula. Wavelet Transforms and Time-Frequency Analysis: The Gabor Transform. Short-Time Fourier Transforms and the Uncertainty Principle. The Integral Wavelet Transform. Dyadic Wavelets and Inversions. Frames. Wavelet Series. Cardinal Spline Analysis: Cardinal Spline Spaces. B-Splines and Their Basic Properties. The Two-Scale Relation and an Interpolatory Graphical Display Algorithm. B-Net Representations and Computation of Cardinal Splines. Construction of Spline Approximation Formulas. Construction of Spline Interpolation Formulas. Scaling Functions and Wavelets: Multiresolution Analysis. Scaling Functions with Finite Two-Scale Relations. Direct-Sum Decompositions of L2(R). Wavelets and Their Duals. Linear-Phase Filtering. Compactly Supported Wavelets. Cardinal Spline-Wavelets: Interpolaratory Spline-Wavelets. Compactly Supported Spline-Wavelets. Computation of Cardinal Spline-Wavelets. Euler-Frobenius Polynomials. Error Analysis in Spline-Wavelet Decomposition. Total Positivity, Complete Oscillation, Zero-Crossings. Orthogonal Wavelets and Wavelet Packets: Examples of Orthogonal Wavelets. Identification of Orthogonal Two-Scale Symbols. Construction of Compactly Supported Orthogonal Wavelets. Orthogonal Wavelet Packets. Orthogonal Decomposition of Wavelet Series. Notes. References. Subject Index. Appendix.
3,992 citations
TL;DR: It is proven that these B-spline wavelets converge to Gabor functions (modulated Gaussian) pointwise and in all L/sub p/-norms with 1 > 1.
Abstract: A family of nonorthogonal polynomial spline wavelet transforms is considered. These transforms are fully reversible and can be implemented efficiently. The corresponding wavelet functions have a compact support. It is proven that these B-spline wavelets converge to Gabor functions (modulated Gaussian) pointwise and in all L/sub p/-norms with 1 >
316 citations
TL;DR: This paper presents an extension of the family of orthogonal Battle/Lemarie spline wavelet transforms with emphasis on filter bank implementation, and considers the special cases of Orthogonal, B-spline, cardinal and dual wavelets.
238 citations