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We consider the variational regularization for inverse problems in a general form. Based on the discrepancy principle, we propose a heuristic parameter choice rule for choosing the regularization parameter which does not require the information on the noise level and is therefore purely data driven. Under variational source conditions, we obtain a posteriori error estimates. According to the Bakushinskii veto, convergence in the worst case scenario cannot be expected in general. However, by imposing certain conditions on the noisy data, we establish a convergence result for the heuristic rule. Applications of the results are addressed and numerical simulations are reported. [ABSTRACT FROM AUTHOR]

Remote sensing images are often contaminated by varying degrees of stripes, which severely affects the visual quality and subsequent application of the data. Unlike with conventional methods, we achieve the destriping by separating the stripe component based on a full analysis of the various stripe properties. Under an optimization framework, an \ell^0-norm-based regularization is used to characterize the global sparse distribution of the stripes. In addition, difference-based constraints are adopted to describe the local smoothness and discontinuity in the along-stripe and across-stripe directions, respectively. The alternating direction method of multipliers is applied to solve and accelerate the model optimization. Experiments with both simulated and real data demonstrate the effectiveness of the proposed model, in terms of both qualitative and quantitative perspectives. [ABSTRACT FROM AUTHOR]