In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class of continuous regularization methods and derive convergence rates under both a-priori and a-posteriori parameter choice rules. Furthermore, we apply our derived results to a standard tomography problem based on the Radon transform.

翻译：在本文中,我们考虑了希尔伯特空间的线性错误问题以及通过框架分解使这些问题正规化的问题,这些问题是单一价值分解的概括性,特别是,我们证明,我们已趋同于一个持续正规化方法的一般类别,并在优先参数选择规则和前卫参数选择规则下得出趋同率。此外,我们还根据拉登变异,将我们得出的结果应用于一个标准的断层摄影问题。