  Inverse problems involving systems of partial differential equations (PDEs)
with many measurements or experiments can be very expensive to solve
numerically. In a recent paper we examined dimensionality reduction methods,
both stochastic and deterministic, to reduce this computational burden,
assuming that all experiments share the same set of receivers. In the present
article we consider the more general and practically important case where
receivers are not shared across experiments. We propose a data completion
approach to alleviate this problem. This is done by means of an approximation
using an appropriately restricted gradient or Laplacian regularization,
extending existing data for each experiment to the union of all receiver
locations. Results using the method of simultaneous sources (SS) with the
completed data are then compared to those obtained by a more general but slower
random subset (RS) method which requires no modifications.
