Imaging of two-dimensional current density distributions from their magnetic field

In this paper we consider different aspects of imaging two-dimensional current density distributions from their magnetic field. Such an imaging is important for its application in nondestructive testing of thin conducting plates. Maps of magnetic fields of currents injected into the plates can be converted through a solution to the inverse problems into images of the currents, and next maps of the conductivity distributions can be created throughout the plates. The inverse problem is equivalent to the solution of the Fredholm integral equation of the first kind, which belongs to the class of ill-posed problems. There is a wide variety of inverse algorithms for such kind of problems. In this paper different methods are compared.