Tomographic inversion using ${\ell }_1$-norm regularization of wavelet coefficients

Abstract

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.

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

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