Temporal Orthogonal Projection Inversion for EMI Sensing of UXO

We present a new approach for inverting time-domain electromagnetic data to recover the location and magnetic dipole polarizations of a limited number of buried objects. We form the multichannel electromagnetic induction (EMI) sensor data as a spatial-temporal response matrix (STRM). The rows of the STRM correspond to measurements sampled at different time channels from one sensor and the columns correspond to measurements sampled at the same time channel from different sensors. The singular value decomposition of the STRM produces the left and right singular vectors that are related to the sensor and the temporal spaces, respectively. If the effective rank of the STRM is r, then the first r singular vectors span signal subspaces (SS), and the remaining singular vectors span the noise subspaces. The original data are projected onto the SS, and the temporal orthogonal projection inversion (TOPI) uses these data in a nonlinear inverse problem to solve for source locations of the objects. The polarizations of the targets are then obtained by solving a linear optimization problem in the original data domain. We present theoretical and numerical analyses to investigate the singular value system of the STRM and the sensitivity of the TOPI to the size of an SS. Only a few subspace vectors are required to generate locations of the objects. The results are insensitive to the exact choice of rank, and this differs from usual methods that involve selecting the number of time channels to be used in the inversion and carefully estimating associated uncertainties. The proposed approach is evaluated using the synthetic and real multistatic EMI data.