Beta Process Factor Analysis for efficient seismic Compressive Sensing with uncertainty quantification

Compressive Sensing for seismic surveys uses sparse signal assumptions to reconstruct the reflected wave field. In the past, most methods utilised dictionaries of fixed basis functions for sparse representation. Recently, algorithms that learn the basis from data are being used with better reconstruction accuracy but longer computational times. One of these is the Beta Process Factor Analysis (BPFA). We propose faster inference for BPFA using Gibbs sampling analysis and illustrate that the reduced computational time does not severely affect the reconstruction accuracy with no aliasing in the frequency spectrum. In addition, associating each prediction with a level of uncertainty is essential but very challenging. Using the Gibbs samples, we create uncertainty maps that are highly correlated with the reconstruction error and are not affected by the faster BPFA inference. Experiments on synthetic and field data illustrate the effectiveness of our proposed methodology for both reconstruction and uncertainty quantification in seismic surveys.