Bayesian feature learning for seismic compressive sensing and denoising

Extracting the maximum possible information from the available measurements is a challenging task but is required when sensing seismic signals in inaccessible locations. Compressive sensing (CS) is a framework that allows reconstruction of sparse signals from fewer measurements than conventional sampling rates. In seismic CS, the use of sparse transforms has some success; however, defining fixed basis functions is not trivial given the plethora of possibilities. Furthermore, the assumption that every instance of a seismic signal is sparse in any acquisition domain under the same transformation is limiting. We use beta process factor analysis (BPFA) to learn sparse transforms for seismic signals in the time slice and shot record domains from available data, and we use them as dictionaries for CS and denoising. Algorithms that use predefined basis functions are compared against BPFA, with BPFA obtaining state-of-the-art reconstructions, illustrating the importance of decomposing seismic signals into learned features.