ABSTRACT An inverse microtomography problem is under consideration in a class of functions with bounded V H variation. An algorithm for solving this problem is proposed based on Tikhonov's regularization with a special regularizer. The algorithm ensures piecewise uniform convergence of approximate solutions to exact solution of the inverse problem. In addition, the question of a-posteriori error estimate of approximate solutions obtained is considered. A new numerical algorithm for finding this estimate is proposed. Numerical experiments on solving a model inverse problem on the class of functions with bounded V H variation are presented along with the results of a-posteriori error estimate for approximate solutions obtained.

中文翻译：

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具有后验误差估计的显微断层扫描逆问题的分段均匀正则化

摘要 在一类具有有界 VH 变化的函数中，正在考虑逆显微断层扫描问题。基于带有特殊正则化器的 Tikhonov 正则化，提出了一种用于解决该问题的算法。该算法确保近似解的分段一致收敛到逆问题的精确解。此外，还考虑了所获得的近似解的后验误差估计问题。提出了一种用于寻找该估计的新数值算法。给出了求解具有有界 VH 变化的函数类的模型逆问题的数值实验以及所获得的近似解的后验误差估计结果。