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.

翻译：本文研究了不规则噪声下线性逆问题的正则化方法。特别地，我们考虑了噪声可通过特定伴随嵌入算子进行预处理的情形。通过引入相应的预处理问题，我们在标准假设下给出了正则化方案的收敛性分析。此外，针对计算机断层扫描中Tikhonov正则化的特例，我们证明该方法可推导出新颖的（基于傅里叶的）滤波反投影算法。采用不同参数选择规则的数值实验验证了所提算法的有效性。