Convergence of regularization methods with filter functions for a regularization parameter chosen with GSURE and mildly ill-posed inverse problems

International audienceIn this work, we show that the regularization methods based on filter functions with a regularization parameter chosen with the GSURE principle are convergent for mildly ill-posed inverse problems and under some smoothness source condition. The convergence rate of the methods is not optimal for very ill-posed problems but the efficiency increases with the smoothness of the solutio