Optimal Experimental Design for the Large‐Scale Nonlinear Ill‐Posed Problem of Impedance Imaging

Many theoretical and practical problems in science involves acquisition of data via an indirect observation (or measurement) of a model or phenomena.Naturally, the observed data are determined by the physical properties of the model sought, as well as the physical laws that governs the problem, however, it is also depends on the experimental configuration. Unlike the model and the physical laws, the last can be controlled by the experimenter. The ability to control the experimental setup is the foundation of optimal experimental design. Optimal experimental design (OED) of well-posed inverse problems is a well established field (e.g., Pukelsheim (2006) and references therein) but, despite the practical necessity, experimental design of ill-posed inverse problems and in particular ill-posed nonlinear problems has remained largely unexplored. We discuss some of the intrinsic differences between welland ill-posed experimental designs,

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