Multiplicative regularization technique for location and shape reconstructions of homogeneous objects

We propose an approach which as compared to binary modified gradient type method by Souriau et al. (1996) or level set type approaches by Litman et al. (see Inverse Probl., no.14, p.685-706, 1998)) is in our opinion simpler. Inspired by our previous work on the inclusions of the total variation (TV) regularizer in van den Berg and Abubakar (Prog. (see Electromag. Research, vol.34, p.189-218, 2002), we propose to include this binary penalty factor as a multiplicative constraint. In this way, the main drawback of this approach can be avoided. In fact. the appropriate regularization parameter is determined by the optimization process itself. The optimization procedure used in this paper is based on the so-called contrast source inversion (CSI) method introduced by van den Berg and Kleinman ((see Inverse Probl., vol.13, p.1607-20, 1997)). Numerical examples demonstrate the robustness and the effectiveness of the CSI method using the binary regularizer. This binary regularizer can further be extended to handle a collection of homogeneous objects having different material parameters. This case is up to now, to our knowledge, not feasible for binary type inversion method. We illustrate this extension with some numerical examples.