Relevance Vector Machines with Uncertainty Measure for Seismic Bayesian Compressive Sensing and Survey Design

Seismic data acquisition in remote locations involves sampling using regular grids of receivers in a field. Extracting the maximum possible information from fewer measurements is cost-effective and often necessary due to malfunctions or terrain limitations. Compressive Sensing (CS) is an emerging framework that allows reconstruction of sparse signals from fewer measurements than conventional sampling rates. In seismic CS, the utilization of sparse solvers has proven to be successful, however, algorithms lack predictive uncertainties. We apply the Relevance Vector Machine (RVM) to seismic CS and propose a novel utilization of multi-scale dictionaries of basis functions that capture different variations in the data. Furthermore, we propose the use of a new predictive uncertainty measure using the information from the neighbours of each estimation to produce accurate uncertainty maps. We apply the RVM to different seismic signals and obtain state-of-the-art reconstruction accuracy. Using the RVM and its predictive uncertainty map, it is possible to quantify risk associated with seismic data acquisition and at the same time guide future survey design.