The objective of the proposed research is to develop structural changes to the design and application of electromagnetic (EM) sensing models to more efficiently and accurately invert EM measurements to extract parameters for applications such as landmine detection. Two different acquisition modalities are addressed in this research: ground-penetrating radar (GPR) and electromagnetic induction (EMI) sensors. The models needed for practical three-dimensional (3D) spatial imaging typically become impractically large, with up to seven dimensions of parameters that need to be extracted. These parameters include, but are not limited to target type, 3D location, and 3D orientation. The new special structures for these models exploit properties such as shift invariance and tensor representation, which can be combined with strategic inversion techniques, including the Fast Fourier Transform and semidefinite programming. The structures dramatically reduce the amount of computation and can eliminate the need to store up to five dimensions of parameters while still accurately estimating them.