On weakly bounded noise in ill-posed problems

We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the error in the data converges strongly to zero, we only assume a type of weak convergence. Under the source conditions that are usually assumed in the presence of convex constraints, we derive optimal convergence rates for convexly constrained Phillips–Tikhonov regularization. We also discuss a version of the Lepskii method for selecting the regularization parameter.

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