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

Project description

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.

Figure 1:
Boundary element model and 13 dipole source model (A), vest-like sensor space (blue) around torso and cryostat-bound sensor space (green) in front of torso (B) and condition numbers of the lead field matrix for a range of sensor quantities (C).

Publications & patents

Eichardt,R., Baumgarten,D., Di Rienzo,L., Linzen,S., Schultze,V., Haueisen,J.: Localisation of buried ferromagnetic objects based on minimum-norm-estimations: a simulation study. COMPEL, 28(5):1323-1333, 2009

Lau,S., Eichardt, R., Di Rienzo,L., Haueisen, J.: Tabu Search Optimization of Magnetic Sensor Systems for Magnetocardiography. IEEE Transactions on Magnetics, 44 (6):1442-1445, 2008

Di Rienzo,L., Haueisen,J.: Numerical Comparison of Sensor Arrays for Magnetostatic Linear Inverse Problems Based on a Projection Method. COMPEL, 26:356-367, 2007

Di Rienzo,L., Haueisen,J.: Theoretical Lower Error Bound for Comparative Evaluation of Sensor Arrays in  Magnetostatic Linear Inverse Problems. IEEE Transactions on Magnetics, 42 (11): 3669-3673, 2006

Di Rienzo,L., Haueisen,J., Arturi,C.M.: Three Component Magnetic Field Data: Impact on Minimum Norm Solutions in a Biomedical Application. COMPEL, 24:869-881, 2005

Arturi,C.M., Di Rienzo,L., Haueisen,J.: Information Content in Single Component versus Three Component Cardiomagnetic Fields. IEEE Transactions on Magnetics, 40(2): 631-634, 2004