Optimization of sensor arrangements during image-guided Lorentz force eddy current testing

Applications of inverse problems techniques abound in medical imaging, seismology, geosciences and many other areas of science and engineering. The solution of inverse problems such as in source reconstruction, source identification or reconstruction of material profiles often requires the use of multiple sensors, typically arranged in sensor arrays. This triggers the question about an optimal number, placement and orientation of these multiple sensors. Figures of merit or error measures in the numerical optimization of the number of sensors included so far least square errors, projections measures or lower error bounds. These measures were commonly restricted to single classes of problems. The central aim of this project is to develop a theoretical framework for existing and newly developed error measures for wide classes of optimization problems. The framework should define an optimal number, placement and orientation of multiple sensors that support a good condition of a lead field matrix and consequently a high stability  of a solution of inverse problem. That optimization of sensor arrays should be applied in Lorentz force eddy current testing, Lorentz force velocimetry, biomedical and other applications.