Isotropic Shearlet Analogs forL2(ℝk) and Localization Operators

DOI10.1080/01630563.2012.682137zbMath1267.42039OpenAlexW1992366839MaRDI QIDQ2919982

Wojciech Czaja, Emily J. King

Publication date: 23 October 2012

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

Full work available at URL: https://doi.org/10.1080/01630563.2012.682137

zbMATH Keywords

representation theorysymplectic matricesshearletslocalization operators

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Multipliers for harmonic analysis in several variables (42B15) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Coherent states (81R30) Unitary representations of locally compact groups (22D10) General harmonic expansions, frames (42C15)

Related Items (14)

Different faces of the shearlet group ⋮ Resolution of the wavefront set using general continuous wavelet transforms ⋮ Simplified vanishing moment criteria for wavelets over general dilation groups, with applications to abelian and shearlet dilation groups ⋮ A classification of continuous wavelet transforms in dimension three ⋮ Geometric classification of semidirect products in the maximal parabolic subgroup of Sp(2, ℝ) ⋮ Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings ⋮ Reproducing subgroups of \(\mathrm{Sp}(2,\mathbb R)\). II: Admissible vectors ⋮ On the range of Stockwell transforms ⋮ Reproducing subgroups of \(Sp(2,\mathbb{R})\). I: Algebraic classification ⋮ Anisotropic shearlet transforms for L² ⋮ Extensions of the Heisenberg group by one‐parameter groups of dilations which are subgroups of the affine and the symplectic groups ⋮ Rotationally invariant time-frequency scattering transforms ⋮ Two-dimensional Shannon type expansions via one-dimensional affine and wavelet lattice actions ⋮ Continuous Stockwell transform: Coherent states and localization operators

Uses Software

• ShearLab

Cites Work

• Analysis and detection of surface discontinuities using the 3D continuous shearlet transform
• Time-frequency partitions and characterizations of modulation spaces with localization operators
• Shearlet coorbit spaces and associated Banach frames
• Sparse directional image representations using the discrete shearlet transform
• The continuous shearlet transform in arbitrary space dimensions
• Radon transform inversion using the shearlet representation
• On Toeplitz-type operators related to wavelets
• On the structure of Bergman and poly-Bergman spaces
• Brushlets: A tool for directional image analysis and image compression
• The continuous wavelet transform and symmetric spaces
• Wedgelets: Nearly minimax estimation of edges
• Foundations of time-frequency analysis
• Abstract harmonic analysis of continuous wavelet transforms
• New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction
• Analytic features of reproducing groups for the metaplectic representation
• Minimally supported frequency composite dilation wavelets
• Analysis of the affine transformations of the time-frequency plane
• Digital Shearlet Transforms
• Characterization and Analysis of Edges Using the Continuous Shearlet Transform
• Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis
• Resolution of the wavefront set using continuous shearlets
• Time-frequency localization operators: a geometric phase space approach
• 𝐿^{𝑝} boundedness of localization operators associated to left regular representations
• Wavelets from Square-Integrable Representations
• Wavelet frames and admissibility in higher dimensions
• A Shearlet Approach to Edge Analysis and Detection
• Optimally Sparse Multidimensional Representation Using Shearlets
• Bandelet Image Approximation and Compression

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