The relevance vector machine for seismic Bayesian compressive sensing

Missing traces in seismic surveys create gaps in the data and cause problems in later stages of the seismic processing workflow through aliasing or incoherent noise. Compressive sensing (CS) is a framework that encompasses data reconstruction algorithms and acquisition processes. However, CS algorithms are mainly ad hoc by focusing on data reconstruction without any uncertainty quantification or feature learning. To avoid ad hoc algorithms, a probabilistic data-driven model is used, the relevance vector machine (RVM), to reconstruct seismic data and simultaneously quantify uncertainty. Modeling of sparsity is achieved using dictionaries of basis functions, and the model remains flexible by adding or removing them iteratively. Random irregular sampling with time-slice processing is used to reconstruct data without aliasing. Experiments on synthetic and field data sets illustrate its effectiveness with state-of-the-art reconstruction accuracy. In addition, a hybrid approach is used in which the domain of operation is smaller while, simultaneously, learned dictionaries of basis functions from seismic data are used. Furthermore, the uncertainty in predictions is quantified using the predictive variance of the RVM, obtaining high uncertainty when the reconstruction accuracy is low and vice versa. This could be used for the evaluation of source/receiver configurations guiding seismic survey design.