Sparsity and level set regularization for near-field electromagnetic imaging in 3D

In this paper, we propose and compare two novel reconstruction strategies for near-field electromagnetic imaging of regions in 3D surrounded by walls or shields. Our focus is on the estimation of electrical conductivity profiles inside regions which are roughly equivalent in size to small rooms or medium-sized containers, from electromagnetic data obtained at one given frequency. This setup has interesting applications in the surveillance of activities behind walls, the screening of boxes or containers at ports or airports, or the monitoring of processes inside regions which might contain hazardous materials. Moreover, the techniques proposed here can easily be adjusted to imaging situations at larger or smaller scale; as often found in geophysical or non-destructive testing applications. The two novel regularization techniques proposed here are based on a sparsity promoting regularization scheme on the one hand, and a level set based shape evolution technique on the other. In our numerical simulations, we perform 3D reconstructions from noisy simulated data and compare the results with those obtained from a standard L2-type reconstruction approach. Our results suggest, in the applications considered here, that the two proposed novel schemes are potentially able to yield significantly improved reconstructions compared to more traditional techniques.