Abstract

While the advent of fast compute is making wave-equation based imaging & inversion a reality, many challenges remain making. By means of examples in linearized imaging and nonlinear full-waveform inversion, we will demonstrate how certain structure-promoting constraints can be used to speed up the calculations and to mitigate adverse affects of local minima. More specifically, we will show that for problems that involve the inversion of expensive to evaluate Jacobians, linearized Bregman iterations, which solve problems with mixed l1-l2 objectives, continue to make progress under randomized subsampling whereas standard (projected) gradients do not. We will also discuss how the adverse affects of local minima in full-waveform inversion can be overcome via structure-promoting constraints. In particular, we review the advantages of working with multiple “simple” constraints instead of with penalties as is more commonly done.