A hybrid stocahstic-deterministic method for waveform inversion

A lot of seismic and medical imaging problems can be written as a least-squares data- fitting problem. In particular, we consider the case of multi-experiment data, where the data consists of a large number of "independent" measurements. Solving the inverse problem then involves repeatedly forward modeling the data for each of these experiments. In case the number of experiments is large and the modeling kernel expensive to apply, such an approach may be prohibitively expensive. We review techniques from stochastic optimization which aim at dramatically reducing the number of experiments that need to be modeled at each iteration. This reduction is typically achieved by randomly subsampling the data. Special care needs to be taken in the optimization to deal with the stochasticity that is introduced in this way.