Construction of Parseval wavelets from redundant filter systems

DOI10.1063/1.1982768zbMath1110.42007arXivmath/0405301OpenAlexW2007506722MaRDI QIDQ3438565

Lawrence W. Baggett, Palle E. T. Jorgensen, Judith A. Packer, Kathy D. Merrill

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405301

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (19)

Hilbert spaces built on a similarity and on dynamical renormalization ⋮ Extension principles for dual multiwavelet frames of \(L_2(\mathbb R^s)\) constructed from multirefinable generators ⋮ The geometry and the analytic properties of isotropic multiresolution analysis ⋮ Multiresolution wavelet analysis of integer scale Bessel functions ⋮ SVD properties of orthogonal two-channel filter banks ⋮ Orthonormal dilations of parseval wavelets ⋮ Harmonic analysis of iterated function systems with overlap ⋮ Probability measures on solenoids corresponding to fractal wavelets ⋮ A characterization of semiorthogonal Parseval wavelets in abstract Hilbert spaces ⋮ Data-driven tight frame construction and image denoising ⋮ Direct limits, multiresolution analyses, and wavelets ⋮ Localized bases in \(L^2(0,1)\) and their use in the analysis of Brownian motion ⋮ Classification of generalized multiresolution analyses ⋮ A non-MRA \(c^r\) frame wavelet with rapid decay ⋮ Generalized multiresolution analyses with given multiplicity functions ⋮ Dimension functions of rationally dilated GMRAs and wavelets ⋮ Homogeneous wavelets and framelets with the refinable structure ⋮ Construction and reconstruction of tight framelets and wavelets via matrix mask functions ⋮ Generalized filters, the low-pass condition, and connections to multiresolution analyses

Cites Work

• Unnamed Item
• Wavelets through a looking glass. The world of the spectrum
• Simple \(C^*\)-algebras generated by isometries
• The theory of multiresolution analysis frames and applications to filter banks
• Adsorbing staircase walks and staircase polygons
• Affine systems in \(L_ 2(\mathbb{R}^d)\): The analysis of the analysis operator
• On dual wavelet tight frames
• Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale \(N\)
• Riesz wavelets and generalized multiresolution analyses.
• The construction of wavelets from generalized conjugate mirror filters in \(L^2(\mathbb R^n)\)
• Framelets: MRA-based constructions of wavelet frames
• Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for \(L^2(\mathbb R{^d})\)
• General existence theorems for orthonormal wavelets, an abstract approach
• Generalized multi-resolution analyses and a construction procedure for all wavelet sets in \(\mathbb{R}^n\)
• Frames and Single Wavelets for Unitary Groups
• Tight frames of compactly supported affine wavelets
• Ten Lectures on Wavelets
• Correcteurs proportionnels-intégraux généralisés
• Hilbert spaces of martingales supporting certain substitution-dynamical systems
• On the dimension function of orthonormal wavelets
• On frame wavelets associated with frame multiresolution analysis
• A characterization of dimension functions of wavelets
• Smooth wavelet tight frames with zero moments
• Generalized low pass filters and MRA frame wavelets

This page was built for publication: Construction of Parseval wavelets from redundant filter systems