Magnetostatic linear inverse problems based on the measurement of magnetic fields arise in a variety of applications, e.g. magneto fluid dynamics, current measurement in multistrands superconducting cables, nondestructive testing, magnetic fields characterization, reconstruction of a magnetization distribution or of the electrical activity in the brain or in the heart.
These problems may be overdetermined (i.e. the number of measurements is higher than the number of unknown parameters) or underdetermined and ill posed. The solution is commonly obtained with the help of regularization.
An important question which arises in practical applications is where magnetic sensors must be located and how many are required. In particular often it is also the case one has to choose between existing or predefined magnetic sensor arrays. It is hence important to define theoretical criteria to compare sensor arrays efficiency for this kind of problems.
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