Gravimetric Anomaly Detection Using Compressed Sensing

• Activity Number: 488
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Government Statistics Section
• Author(s): Hoyt Koepke* and Ryan Kappedal and Marina Meila
• Companies: University of Washington and Air Force Institute of Technology and University of Washington
• Keywords: compressed sensing ; dictionary learning ; gravimetry ; L1 minimization ; sparse recovery

Abstract

We address the problem of identifying underground anomalies (e.g. holes) based on gravity measurements. This is a theoretically well-studied yet difficult problem. In all except a few special cases, the inverse problem has multiple solutions, and additional constraints are needed to regularize it. Our approach makes general assumptions about the shape of the anomaly that can also be seen as sparsity assumptions. We can then adapt recently developed sparse reconstruction algorithms to address this problem. The results are extremely promising, even though the theoretical assumptions underlying sparse recovery do not hold for gravity problems of this kind. We examine several types of sparse bases in the context of this gravity inverse problem and compare and contrast their relative merits.