Tomographic inversion using ℓ1-norm regularization of wavelet coefficients

We propose the use of ℓ₁ 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.