论文标题
关于双帧的描述
On Description of Dual Frames
论文作者
论文摘要
使用帧的信号重建过程中的关键问题之一是找到双帧。通常，使用规范的双框架。但是，在许多应用程序中，这种选择似乎是不幸的。由于这一事实，有必要开发一种工具，这有助于找到合适的双重框架。在本文中，我们提供了一种方法来查找每个双帧。所提出的方法基于Naimark的扩张定理，对二帧的描述涉及将parseval框架扩展到正统基础的参数。这些公式可简化有限维空间和近瑞斯基地的框架。在后一种情况下，简化基于Naimark定理的扩展和补充版本，该版本在本文的最后一部分中得到了证明。
One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that fact, it is necessary to develop a tool, which helps to find a suitable dual frame. In this paper we give a method to find every dual frames. The proposed method is based on Naimark's dilation theorem and the obtained description of dual frames involves parameters that characterize extension of a Parseval frame to an orthonormal basis. These formulas are simplified for frames in finite-dimensional spaces and for near-Riesz bases. In the latter case, the simplification is based on the extended and supplemented version of the Naimark theorem, which is proved in the last part of the paper.
