Tomographic inversion using $\ell_1$-norm regularization of wavelet coefficients

Details Tomographic inversion using $\ell_1$-norm regularization of wavelet coefficients Tomographic inversion using $\ell_1$-norm regularization of wavelet coefficients

2006-08-08

arxiv.org/abs/physics/0608094v1

Geophysical Journal International 170 (2007) 359-370

Physics

Geophysics

19 pages, 14 figures. Submitted to GJI July 2006. This preprint does not use GJI style files (which gives wrong received/accep

Scientific paper

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

We propose the use of $\ell_1$ 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.

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