  Modern-day seismic imaging and monitoring technology increasingly rely on
dense full-azimuth sampling. Unfortunately, the costs of acquiring densely
sampled data rapidly become prohibitive and we need to look for ways to
sparsely collect data, e.g. from sparsely distributed ocean bottom nodes, from
which we then derive densely sampled surveys through the method of wavefield
reconstruction. Because of their relatively cheap and simple calculations,
wavefield reconstruction via matrix factorizations has proven to be a viable
and scalable alternative to the more generally used transform-based methods.
While this method is capable of processing all full azimuth data frequency by
frequency slice, its performance degrades at higher frequencies because
monochromatic data at these frequencies is not as well approximated by low-rank
factorizations. We address this problem by proposing a recursive recovery
technique, which involves weighted matrix factorizations where recovered
wavefields at the lower frequencies serve as prior information for the recovery
of the higher frequencies. To limit the adverse effects of potential
overfitting, we propose a limited-subspace recursively weighted matrix
factorization approach where the size of the row and column subspaces to
construct the weight matrices is constrained. We apply our method to data
collected from the Gulf of Suez, and our results show that our limited-subspace
weighted recovery method significantly improves the recovery quality.
