Optimal Experimental Design for the Large-Scale Nonlinear Ill-posed Problem of Impedance Imaging

Many theoretical and practical problems in science involve acquisition of data via indirect observations of a model or phenomena. Naturally, the observed data are determined by the physical properties of the model sought, as well as by the physical laws that govern the problem, however, they also depend on the experimental configuration. Unlike the model and the physical laws, the latter can be controlled by the experimenter. It is this possibility of controlling the experimental setup that leads to optimal experimental design (OED). Optimal experimental design of well-posed inverse problems is a well established field (e.g., Fedorov (1972); Pukelsheim (2006) and references therein), yet, despite the practical necessity, experimental design of ill-posed inverse problems and in particular ill-posed nonlinear problems has remained largely unexplored. We