Augmented Lagrangian Based Full-waveform Inversion with Anderson Acceleration

Abstract

Summary The augmented Lagrangian (AL) method allows an efficient solution of full-waveform inversion (FWI). It is robust with respect to the initial model while being general (in the sense of dealing which non-differentiable (e.g., TV) regularizers) and decomposable (which makes it suitable for dealing with large scale problems). The method, however, behaves more like a first-order method than a second-order method, and thus a natural extension of the method is in the direction of improving its convergence rate. In this abstract, we consider the possibility of accelerating the AL-based FWI with sophisticated acceleration strategies. The algorithm is recast as a fixed-point iteration, which enables us to apply acceleration schemes. In particular, Anderson acceleration is applied, which stores the information from previous iterates and uses their linear combination with the current iterate to increase the convergence rate. The numerical examples show improvements in both the convergence rate and the quality of the final solution compared with the traditional iteratively refined wavefield reconstruction inversion.