论文标题
双帧补偿擦除 - 非规范案例
Dual frames compensating for erasures -- non-canonical case
论文作者
论文摘要
在本文中，我们研究了从擦除框架系数中恢复信号的问题。假设删除的系数由有限的集合$ e $索引。从框架$（x_n）_ {n = 1}^\ intty $及其任意双重帧开始，我们给出了足够的条件来构建$（x_n）_ {n \ in E^c} $的双帧，以便可以从保留的框架系数中获得完美的重建。这项工作是通过使用$（x_n）_ {n = 1}^\ infty $的规范双重框架的方法来激励的，但是，该$并未自动扩展到使用另一个双重框架替换规范双重的情况。开始二元框时的案例之间的差异是规范双重二元组，而不是规范双重的偶数。我们还提供了几种计算二元框架双重框架的方法，其中我们对计算此双重帧的迭代过程最感兴趣。计算测试表明，在某些情况下，迭代算法的性能比其他考虑的程序更快。
In this paper we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased coefficients are indexed by a finite set $E$. Starting from a frame $(x_n)_{n=1}^\infty$ and its arbitrary dual frame, we give sufficient conditions for constructing a dual frame of $(x_n)_{n\in E^c}$ so that the perfect reconstruction can be obtained from the preserved frame coefficients. The work is motivated by methods using the canonical dual frame of $(x_n)_{n=1}^\infty$, which however do not extend automatically to the case when the canonical dual is replaced with another dual frame. The differences between the cases when the starting dual frame is the canonical dual and when it is not the canonical dual are investigated. We also give several ways of computing a dual of the reduced frame, among which we are the most interested in the iterative procedure for computing this dual frame. Computational tests show that in certain cases the iterative algorithm performs faster than the other considered procedures.
