An algebraic perspective on multivariate tight wavelet frames

DOI10.1007/s00365-013-9191-5zbMath1279.65146OpenAlexW1981295076MaRDI QIDQ378141

Joachim Stöckler, Maria Charina, Mihai Putinar, Claus Scheiderer

Publication date: 11 November 2013

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-013-9191-5

zbMATH Keywords

semidefinite programmingLaurent polynomialsreal algebraic geometrywavelet frameexistence of tight wavelet framesmultivariate tight wavelet framenumerical construction of tight wavelet framesunitary extension principle

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Semidefinite programming (90C22) Nonconvex programming, global optimization (90C26) Sums of squares and representations by other particular quadratic forms (11E25) Numerical methods for wavelets (65T60) General harmonic expansions, frames (42C15) Real algebraic and real-analytic geometry (14P99)

Related Items (13)

On extensions of wavelet systems to dual pairs of frames ⋮ Dual Gramian analysis: Duality principle and unitary extension principle ⋮ New constructions of nonseparable tight wavelet frames ⋮ Quasi-tight framelets with high vanishing moments derived from arbitrary refinable functions ⋮ Symmetric canonical quincunx tight framelets with high vanishing moments and smoothness ⋮ Tight wavelet filter banks with prescribed directions ⋮ Multivariate tight wavelet frames with few generators and high vanishing moments ⋮ A structural characterization of compactly supported OEP-based balanced dual multiframelets ⋮ Interpolatory tight wavelet frames with prime dilation ⋮ On construction of multivariate Parseval wavelet frames ⋮ An algebraic perspective on multivariate tight wavelet frames. II ⋮ Multivariate quasi-tight framelets with high balancing orders derived from any compactly supported refinable vector functions ⋮ Scaling Laplacian Pyramids

Cites Work

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• Wavelet frame based blind image inpainting
• Construction of multivariate compactly supported tight wavelet frames
• Tight wavelet frames for irregular multiresolution analysis
• Tight wavelet frames for subdivision
• Constructing tight frames of multivariate functions
• Accuracy of lattice translates of several multidimensional refinable functions
• Box splines
• Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
• Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale \(N\)
• Triangular \(\sqrt 3\)-subdivision schemes: The regular case
• Sums of squares on real algebraic curves
• Adaptive wavelet methods. II: Beyond the elliptic case
• Compactly supported tight and sibling frames with maximum vanishing moments
• Multiwavelet frames from refinable function vectors
• Framelets: MRA-based constructions of wavelet frames
• Tight wavelet frames via semi-definite programming
• Sums of squares on real algebraic surfaces
• Tight frames of compactly supported multivariate multi-wavelets
• Positivity and Optimization: Beyond Polynomials
• A butterfly subdivision scheme for surface interpolation with tension control
• Ten Lectures on Wavelets
• Tight compactly supported wavelet frames of arbitrarily high smoothness
• Adaptive wavelet methods for elliptic operator equations: Convergence rates
• Sums of squares of regular functions on real algebraic varieties
• Smooth wavelet tight frames with zero moments
• Construction of multivariate tight frames via Kronecker products

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