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We propose a new stopping criterion for Krylov subspace iterativeregularization of large-scale ill-posed inverse problems. Our stoppingcriterion accurately filters the data using a generalization of the Picardparameter that was originally introduced for direct regularization ofsmall-scale problems. In the one dimension we filter the data in the discreteFourier transform (DFT) basis using the Picard parameter, which separatesnoise-dominated Fourier coefficients from the signal-dominated ones. Fortwo-dimensional problems we propose a novel vectorization scheme of the Fouriercoefficients of the data based on the Kronecker product structure of thetwo-dimensional DFT matrix, which effectively reduces the problem to onedimension. At each iteration we compute the distance between the datareconstructed from the iterated solution and the filtered data, terminating theiterations once this distance begins to increase or to level off. The accuracyand robustness of the proposed method is demonstrated by several numericalexamples and a MATLAB-based implementation is provided.

Stopping criterion for iterative regularization of large-scale ill-posed problems using the Picard parameter