Tomographic inversion using ℓ1-norm regularization of wavelet coefficients

Abstract

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.