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The problem of reconstructing a two-dimensional (2D) current distribution ina superconductor from a 2D magnetic field measurement is recognized as afirst-kind integral equation and resolved using the method of Regularization.Regularization directly addresses the inherent instability of this inversionproblem for non-exact (noisy) data. Performance of the technique is evaluatedfor different current distributions and for data with varying amounts of addednoise. Comparisons are made to other methods, and the present method isdemonstrated to achieve a better regularizing (noise filtering) effect whilealso employing the generalized-cross validation (GCV) method to choose theoptimal regularization parameter from the data, without detailed knowledge ofthe true (and generally unknown) solution. It is also shown that clean,noiseless data is an ineffective test of an inversion algorithm.Comment: To appear in the Physical Review B. Some text/figure additions and  modification

Resolution of two-dimensional currents in superconductors from a two-dimensional magnetic field measurement by the method of regularization