Non-commutative affine geometry and symbol calculus: Fourier transform magnetic resonance imaging and wavelets

DOI10.1007/BF03322260zbMath0844.92011OpenAlexW2092350936MaRDI QIDQ1904441

Walter Johannes Schempp

Publication date: 29 August 1996

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03322260

zbMATH Keywords

Radon transformmedical imagingpseudodifferential operatorsSchwartz kernelstransvectantsnon-commutative Fourier analysisquantum holographyHeisenberg nilpotent Lie groupaffine solvable Lie group GA(R)distributional harmonic analysisFourier transform magnetic resonance imaginginfinitesimal generator of smooth dynamical systemsLauterbur spatial encoding techniqueneurodiagnostic imagingnon-commutative geometry of affine transvectionsnon-invasive radiodiagnosticsplanar coadjoint orbit stratificationresonance of affine waveletssemi-classical approachsymplectic Fourier transform inversionsymplectic MRI filter bank processingsymplectically invariant symbol calculus

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Biomedical imaging and signal processing (92C55) Radon transform (44A12) Electromagnetic interaction; quantum electrodynamics (81V10) Applications of Lie groups to the sciences; explicit representations (22E70) Geometry and quantization, symplectic methods (81S10) Analysis on other specific Lie groups (43A80)

Cites Work

• Cyclic cohomology for one-parameter smooth crossed products
• Sur certains groupes d'opérateurs unitaires
• Phase coherent wavelets, Fourier transform magnetic resonance imaging, and synchronized time-domain neural networks
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• Square Integrable Representations of Unimodular Groups
• When is a Kirillov Orbit a Linear Variety?
• The weyl calculus of pseudo-differential operators
• Pick's Formula via the Weierstrass ℘-Function
• Square Integrable Representations of Nilpotent Groups
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