Polyharmonic multiresolution analysis: An overview and some new results

DOI10.1007/s11075-008-9173-zzbMath1153.65130OpenAlexW2060042967MaRDI QIDQ937171

Christophe Rabut, Milvia Rossini

Publication date: 20 August 2008

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9173-z

zbMATH Keywords

waveletsconvergencemultiresolution analysisB-splinespolyharmonic splinesdecomposition and reconstruction filtersMRA filterpolyharmonic scaling functionsscattered data wavelet

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical methods for wavelets (65T60)

Related Items (7)

Generalized Whittle-Matérn and polyharmonic kernels ⋮ Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters ⋮ Properties of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines ⋮ Construction of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines ⋮ Quasi-interpolation operators on hexagonal grids with high approximation orders in spaces of polyharmonic splines ⋮ On MRAs and prewavelets based on elliptic splines ⋮ Interpolation of data functions on parallel hyperplanes

Uses Software

• Algorithm 792

Cites Work

• Polyharmonic cardinal splines
• On the construction of polyharmonic \(B\)-splines
• Elementary \(m\)-harmonic cardinal B-splines
• High level \(m\)-harmonic cardinal B-splines
• Using the refinement equation for the construction of pre-wavelets. III: Elliptic splines
• Approximating surfaces with discontinuities.
• Decomposition and reconstruction of multidimensional signals using polyharmonic pre-wavelets
• A characterization of wavelet convergence in sobolev spaces
• Radial Basis Functions
• Algorithm 792
• Self-Similarity: Part II—Optimal Estimation of Fractal Processes
• ON THE ERRORS OF MULTIDIMENSIONAL MRA BASED ON NON-SEPARABLE SCALING FUNCTIONS
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• Unnamed Item
• Unnamed Item
• Unnamed Item

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