In this paper; we propose a new approach to solve the magnetostatic inverse problem. The goal of the work is, from measurements of the magnetic field in the air; to rebuild a model for the magnetization of a ferromagnetic shell structure. It's then possible to calculate the field where sensors cannot be placed. This problem is usually ill posed or rank-deficient, it's then necessary to use mathematical regularizations. These techniques are based upon the injection of knowledge about the mathematical behavior of the solution. We preferred to add physical information. This solution allows us to get a faithful solution and to reduce significantly the number of sensors. Moreover; our method has been tested on a mock-up with real measurements and led to very promising results.
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