Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion

Frederik Jozef Simons; Ignace Loris; Eugene Brevdo; Ingrid C. Daubechies

doi:10.1117/12.892285

Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion

Frederik Jozef Simons, Ignace Loris, Eugene Brevdo, Ingrid C. Daubechies

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

11 Scopus citations

Abstract

Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.

Original language	English (US)
Title of host publication	Wavelets and Sparsity XIV
DOIs	https://doi.org/10.1117/12.892285
State	Published - 2011
Event	Wavelets and Sparsity XIV - San Diego, CA, United States Duration: Aug 21 2011 → Aug 24 2011

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	8138
ISSN (Print)	0277-786X

Other

Other	Wavelets and Sparsity XIV
Country	United States
City	San Diego, CA
Period	8/21/11 → 8/24/11

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

Keywords

frames
geophysics
inverse theory
localization
sparsity
spherical harmonics
wavelets

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10.1117/12.892285

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year = "2011",

doi = "10.1117/12.892285",

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Simons, FJ, Loris, I, Brevdo, E & Daubechies, IC 2011, Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion. in Wavelets and Sparsity XIV., 81380X, Proceedings of SPIE - The International Society for Optical Engineering, vol. 8138, Wavelets and Sparsity XIV, San Diego, CA, United States, 8/21/11. https://doi.org/10.1117/12.892285

Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion. / Simons, Frederik Jozef; Loris, Ignace; Brevdo, Eugene; Daubechies, Ingrid C.

Wavelets and Sparsity XIV. 2011. 81380X (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8138).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion

AU - Simons, Frederik Jozef

AU - Loris, Ignace

AU - Brevdo, Eugene

AU - Daubechies, Ingrid C.

PY - 2011

Y1 - 2011

N2 - Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.

AB - Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.

KW - frames

KW - geophysics

KW - inverse theory

KW - localization

KW - sparsity

KW - spherical harmonics

KW - wavelets

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M3 - Conference contribution

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T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - Wavelets and Sparsity XIV

T2 - Wavelets and Sparsity XIV

Y2 - 21 August 2011 through 24 August 2011

ER -

Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion

Abstract

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All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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