Open AccessTomographic inversion using ℓ 1 ‐norm regularization of wavelet coefficients
Author(s) -
Loris Ignace,
Nolet Guust,
Daubechies Ingrid,
Dahlen F. A.
Publication year - 2007
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2007.03409.x
Subject(s) - classification of discontinuities , wavelet , regularization (linguistics) , mathematics , tomography , inverse problem , inversion (geology) , basis pursuit , inverse theory , algorithm , mathematical analysis , geology , computer science , compressed sensing , physics , optics , seismology , artificial intelligence , matching pursuit , surface wave , tectonics
SUMMARY We propose the use of ℓ 1 regularization in a wavelet basis for the solution of linearized seismic tomography problems A m = 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.