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Tomographic inversion using ℓ1-norm regularization of wavelet coefficients

Publication ,  Journal Article
Loris, I; Nolet, G; Daubechies, I; Dahlen, FA
Published in: Geophysical Journal International
July 1, 2007
Published version (DOI)

We propose the use of ℓ1 regularization in a wavelet basis for the solution of linearized seismic tomography problems Am = d, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution m that contains no more fine-scale structure than is necessary to fit the data d to within its assigned errors. © 2007 The Authors Journal compilation © 2007 RAS.

Duke Scholars

Ingrid Daubechies
Author Ingrid Daubechies Mathematics

Published In

Geophysical Journal International

DOI

10.1111/j.1365-246X.2007.03409.x

EISSN

1365-246X

ISSN

0956-540X

Publication Date

July 1, 2007

Volume

170

Issue

1

Start / End Page

359 / 370

Related Subject Headings

  • Geochemistry & Geophysics
  • 4013 Geomatic engineering
  • 3706 Geophysics
  • 3705 Geology
  • 0909 Geomatic Engineering
  • 0404 Geophysics
  • 0403 Geology
 

Citation

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ICMJE
MLA
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Loris, I., Nolet, G., Daubechies, I., & Dahlen, F. A. (2007). Tomographic inversion using ℓ1-norm regularization of wavelet coefficients. Geophysical Journal International, 170(1), 359–370. https://doi.org/10.1111/j.1365-246X.2007.03409.x
Loris, I., G. Nolet, I. Daubechies, and F. A. Dahlen. “Tomographic inversion using ℓ1-norm regularization of wavelet coefficients.” Geophysical Journal International 170, no. 1 (July 1, 2007): 359–70. https://doi.org/10.1111/j.1365-246X.2007.03409.x.
Loris I, Nolet G, Daubechies I, Dahlen FA. Tomographic inversion using ℓ1-norm regularization of wavelet coefficients. Geophysical Journal International. 2007 Jul 1;170(1):359–70.
Loris, I., et al. “Tomographic inversion using ℓ1-norm regularization of wavelet coefficients.” Geophysical Journal International, vol. 170, no. 1, July 2007, pp. 359–70. Scopus, doi:10.1111/j.1365-246X.2007.03409.x.
Loris I, Nolet G, Daubechies I, Dahlen FA. Tomographic inversion using ℓ1-norm regularization of wavelet coefficients. Geophysical Journal International. 2007 Jul 1;170(1):359–370.
Journal cover image

Published In

Geophysical Journal International

DOI

10.1111/j.1365-246X.2007.03409.x

EISSN

1365-246X

ISSN

0956-540X

Publication Date

July 1, 2007

Volume

170

Issue

1

Start / End Page

359 / 370

Related Subject Headings

  • Geochemistry & Geophysics
  • 4013 Geomatic engineering
  • 3706 Geophysics
  • 3705 Geology
  • 0909 Geomatic Engineering
  • 0404 Geophysics
  • 0403 Geology