$\ell_1$ Regularized Inversion

Ben Witten

ben@sep.stanford.edu

ABSTRACT

Here an interior point inversion method is presented that solve a least squares problem with $\ell_1$ regularization. Velocity inversion can benefit from $\ell_1$ regularization because the sparse solution creates blocky velocity models. This is often more geologically accurate than smooth models. In this paper an efficient method is present for solving $\ell_1$ regularized least squares problems. Its usefulness is shown through comparisons of previous methods on an example using a least squares formulation for Dix inversion.