Piecewise Smoothed Value Picking Regularization Applied to 2-D TM and TE Inverse Scattering

The Stepwise Relaxed Value Picking (SRVP) regularization technique, proposed earlier for the iterative reconstruction of piecewise (quasi-)homogeneous objects, is a non-spatial technique, whereby the reconstruction unknowns are clustered around a limited number of—a-priori unknown—reference values. Artifacts have been observed in some 2-D and 3D complex permittivity reconstructions. This paper therefore combines the non-spatial SRVP technique with a spatial smoothing technique, whereby the reference values provided by the former—in each iteration—are employed by the latter to define separate smoothing regions. This way edges are preserved, since the spatial smoothing constraints in the cost function are active within but not across the region boundaries. This combined technique, denoted as Stepwise Relaxed Piecewise Smoothed Value Picking (SRPSVP) regularization, is formulated for the 2.5D microwave inverse scattering problem and is illustrated with reconstructions from the Institut Fresnel 2-D scattering database.