Sparsity enhanced fast subsurface imaging with GPR

Abstract

Sparsity of a signal starts to become very important in many applications. In subsurface imaging, generally potential targets covers a small part of the total subsurface volume to be imaged, thus the targets are spatially sparse. Under this assumption it is shown that the subsurface imaging problem can be formulated as a dictionary selection problem which can be solved quickly using basis pursuit type algorithms compared to previously published convex optimization based methods. Spatial sparsity also indicates that the number of measurements (spatial or time/frequency) that GPR collects can be reduced, decreasing the data acquisition time. Orthogonal matching pursuit algorithm is used for reconstructing sparse subsurface images. Results show that the proposed method reduces time both in data acquisition and processing compared to previous methods with similar performance.