Seismic compressive sensing beyond aliasing using Bayesian feature learning

Sampling the seismic wave field and concurrently obtaining the true underlying signal is a challenging task due to environmental, economical and/or equipment limitations involved in seismic surveys. Under-sampling could alias the signal and Compressive Sensing methods use sparse assumptions to reconstruct it on a denser grid. It is assumed that various predefined dictionaries of basis functions provide a sparse representation of the seismic wave field. However, this is very limiting since different signals could contain different structures that require their own sparse representation. We propose to learn dictionaries of basis functions while interpolating with Beta Process Factor Analysis (BPFA). Comparisons with other solvers are undertaken, and learned basis functions are used by Spectral Projected Gradient for L1 (SPGL1) with the performance evaluated. Furthermore, we show that BPFA is able to reconstruct irregular under-sampled seismic signals without any signs of aliasing in the F/K domain. In addition, a feature space is obtained from millions of learned basis functions that could be used to decompose a seismic signal into features for various tasks in seismic data processing.