Scale continuous, scale discretized, and scale discrete harmonic wavelets for the outer and the inner space of a sphere and their application to an inverse problem in geomathematics

DOI10.1006/acha.2001.0369zbMath0995.42027OpenAlexW1973352912MaRDI QIDQ1604499

Volker Michel

Publication date: 4 July 2002

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/cbae655ca8470d05de20b250c8df647a12e955e7

zbMATH Keywords

inverse problemmultiscale methodsgravimetryisotropic scale continuous waveletsregularization waveletsscale discrete harmonic wavelets

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Inverse problems in geophysics (86A22) Numerical methods for wavelets (65T60)

Related Items (10)

Operator-theoretic and regularization approaches to ill-posed problems ⋮ On mathematical aspects of a combined inversion of gravity and normal mode variations by a spline method ⋮ Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions ⋮ WAVELET DEFORMATION ANALYSIS FOR SPHERICAL BODIES ⋮ Vectorial Slepian Functions on the Ball ⋮ Inverse gravimetry: background material and multiscale mollifier approaches ⋮ Locally supported approximate identities on the unit ball ⋮ Ill-Posed Problems: Operator Methodologies of Resolution and Regularization ⋮ Inverse Gravimetry as an Ill-Posed Problem in Mathematical Geodesy ⋮ Joint Inversion of Multiple Observations

Cites Work

• Constructive approximation and numerical methods in geodetic research today -- an attempt at a categorization based on an uncertainty principle
• Applied mathematics meets signal processing.
• Wavelets on the 2-sphere: A group-theoretical approach
• Spherical wavelet transform and its discretization
• Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
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