论文标题
在Hilbert空间中具有层压仪的框架线性操作员的框架分解
Frame Decompositions of Bounded Linear Operators in Hilbert Spaces with Applications in Tomography
论文作者
论文摘要
我们考虑了在形成帧的功能方面，有界线性算子在希尔伯特空间上的分解。与单数值分解相似，所得的帧分解编码有关该问题的结构和不良性的信息，可以用作设计和实施有效的数值解决方案方法的基础。与奇异值分解相反，所呈现的框架分解可以明确地针对宽类的运算符，尤其是满足一定稳定性条件的人。为了显示这种方法的有用性，我们考虑了层析成像领域的不同示例。
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and ill-posedness of the problem and can be used as the basis for the design and implementation of efficient numerical solution methods. In contrast to the singular-value decomposition, the presented frame decompositions can be derived explicitly for a wide class of operators, in particular for those satisfying a certain stability condition. In order to show the usefulness of this approach, we consider different examples from the field of tomography.
