Low-Rank Matrix Completion for Distributed Ambient Noise Imaging Systems

We present a new approach to address the "missing data" issue in the distributed ambient noise imaging (ANSI) system, a promising new seismic imaging paradigm for shallow earth surfaces. Missing data is inevitable in distributed ANSI: due to communication constraint and weak signals, not all pairs of cross-correlation functions between sensors contain useful information (i.e., a significant peak). Without completing the missing data, we cannot use the conventional ambient noise imaging methods, which requires to know the complete pairs of cross-correlation between sensors. We show that the problem can be formulated as a low-rank matrix completion problem, and leverage the recent advances in this field to present an efficient algorithm. Simulated and real-data examples demonstrate the promising performance of our approach.