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In this paper, we prove optimal convergence rates results for regularisationmethods for solving linear ill-posed operator equations in Hilbert spaces. Theresult generalises existing convergence rates results on optimality to generalsource conditions, such as logarithmic source conditions. Moreover, we alsoprovide optimality results under variational source conditions and show theconnection to approximative source conditions.

Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces