In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent preprocessed problem, we provide convergence analysis for general regularization schemes under standard assumptions. Furthermore, for a special case of Tikhonov regularization in Computerized Tomography, we show that our approach leads to a novel (Fourier-based) filtered backprojection algorithm. Numerical examples with different parameter choice rules verify the efficiency of our proposed algorithm.

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