Families of multiresolution and wavelet spaces with optimal properties

DOI10.1080/01630569308816532zbMath0798.94007OpenAlexW2021144192MaRDI QIDQ4293269

Michael Unser, Akram Al-Droubi

Publication date: 10 November 1994

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569308816532

zbMATH Keywords

waveletsShannon theoryGabor theoryalgebraic properties of the internal convolution productdigital signal representationmultiscale sampling

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items

Oblique and hierarchical multiwavelet bases, Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theory, On the limit of sampled signal extrapolation with a wavelet signal model^∗, Portraits of Frames, Factoring wavelet transforms into lifting steps, The theory of multiresolution analysis frames and applications to filter banks, Approximation error for quasi-interpolators and (multi-)wavelet expansions, Matched wavelets for equidistant points

Cites Work

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• General sampling theorems for functions in reproducing kernel Hilbert spaces
• Cardinal spline filters: Stability and convergence to the ideal sinc interpolator
• A family of polynomial spline wavelet transforms
• Notes on spline functions. III: On the convergence of the inter polating cardinal splines as their degree tends to infinity
• On Lagrange Interpolation and Kramer-Type Sampling Theorems Associated with Sturm–Liouville Problems
• A theory for multiresolution signal decomposition: the wavelet representation
• Five short stories about the cardinal series
• Orthonormal bases of compactly supported wavelets
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• A Simple Wilson Orthonormal Basis with Exponential Decay
• Singularity detection and processing with wavelets
• Image compression through wavelet transform coding
• On the asymptotic convergence of B-spline wavelets to Gabor functions
• A sampling theorem for wavelet subspaces
• Wavelets and filter banks: theory and design
• Biorthogonal bases of compactly supported wavelets
• Continuous and Discrete Wavelet Transforms
• Sampling for Spline Reconstruction
• A Generalized Sampling Theorem
• Applications of reproducing kernel Hilbert spaces–bandlimited signal models