This thesis focuses on monitoring stored grain through the use of electromagnetic inversion. Electromagnetic inversion is the process of illuminating a target with electromagnetic waves, and from limited field measurements attempting to reconstruct the target. Specifically, we aim to obtain an image of grain/air interface inside metallic-walled bins. Finding the grain/air interface is a starting point for full 3-D imaging of stored grain. The methods currently used to estimate the grain/air interface are computationally expensive, and have not been designed to image non-symmetric grain surfaces. To obtain the grain/air interface we studied and applied linear inversion methods, which are typically good at locating material boundaries (but not the exact permittivity of the materials). We use the linear Orthogonality Sampling Method (OSM), which we show is a specific form of back-propagated imaging. The identification of OSM as a back-propagation technique allows us to formulate the linear imaging problem with an arbitrary Green's function, which is a necessary step as grain bins are made of metallic shapes that do not have analytic Green's functions. To test our proposed technique for finding the grain/air interface, we consider a series of 2-D scalar simulations on both simple rectangular and grain bin-cross section-shaped boundaries. To compute our fields and numerical Green's functions, we use a Discontinuous Galerkin Method (DGM) solver. Initially applying the back-propagation technique in a background material of free space does not lead to reasonable results: images that should show the grain/air interface instead closely resembled the resonant modes of the electromagnetic fields inside the bin. To address this problem, we switch the background medium used in the back-propagation algorithm to closely resemble the permittivity of the grain. In this case, we could obtain reasonable images of the grain/air interface in our simulations. In brief, we show that using a Green's function associated with a bin full of grain instead of air provides images in which the grain surface is discernible. In an effort to improve the results, we created a solution to the back-propagated image that used whole-domain Fourier basis functions instead of pulse-basis functions. This technique failed when reconstituting 2-D bin models with a low amount of grain. On the whole, the main contribution of this thesis is the realization that for PEC bounded problems, back-propagation-based algorithms do not work well. However, by assuming a convenient background (that introduces loss), one can drastically improve the final reconstructed results of back-propagation-based algorithms.