Characterization of Oblique Dual Frame Pairs
Characterization of Oblique Dual Frame Pairs
复制标题
DOI：
10.1155/asp/2006/92674
复制
发表时间：
2006
影响因子：
1.9
通讯作者：
Yonina C. Eldar;O. Christensen
中科院分区：
文献类型：
--
作者：
Yonina C. Eldar;O. Christensen
给定一个Hilbert空间的子空间的框架，我们考虑在适当选择的子空间上的所有可能的斜对偶框架向量族。代替标准的描述，这涉及到计算的伪逆的框架运营商，我们开发了一种替代的表征，在某些情况下，可以计算更有效。我们首先处理的情况下，一个一般的框架在任意的希尔伯特空间，然后专门的结果，移动不变的框架与多个发电机。特别是，我们提出了明确的版本，我们的一般条件的情况下，移位不变的空间与一个单一的发电机。该理论还适用于标准框架设置，其中原始框架和双重框架定义在同一空间上。
Given a frame for a subspace of a Hilbert space, we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace. In place of the standard description, which involves computing the pseudoinverse of the frame operator, we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a general frame on an arbitrary Hilbert space, and then specialize the results to shift-invariant frames with multiple generators. In particular, we present explicit versions of our general conditions for the case of shift-invariant spaces with a single generator. The theory is also adapted to the standard frame setting in which the original and dual frames are defined on the same space.