Linearly connected sequences and spectrally optimal dual frames for erasures
Linearly connected sequences and spectrally optimal dual frames for erasures
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DOI：
10.1016/j.jfa.2013.08.012
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发表时间：
2013-12
影响因子：
1.7
通讯作者：
Saliha Pehlivan;D. Han;R. Mohapatra
中科院分区：
文献类型：
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作者：
Saliha Pehlivan;D. Han;R. Mohapatra
在一个帧被指定用于应用并且在数据传输过程中发生擦除的情况下，我们研究了从单个擦除恢复的最佳双帧。与以前的文献不同，我们把误差算子的谱半径而不是它的算子范数作为最优性的度量。当诺依曼级数用于以迭代方式恢复原始数据时，这种最优化概念是很自然的。根据给定帧的冗余度分布，我们得到了谱一擦最优对偶帧的完全刻画。我们的刻画依赖于擦除最优帧与帧的线性连通性之间的联系。证明了线性连通性等价于交相关性质，并与著名的AK-无关集的概念密切相关。此外，我们还建立了交替对偶框架存在的几个充要条件，使迭代重建工作。
In the case that a frame is prescribed for applications and erasures occur in the process of data transmissions, we examine optimal dual frames for the recovery from single erasures. In contrast to earlier papers, we consider the spectral radius of the error operator instead of its operator norm as a measure of optimality. This notion of optimality is natural when the Neumann series is used to recover the original data in an iterative manner. We obtain a complete characterization of spectrally one-erasure optimal dual frames in terms of the redundancy distribution of the prescribed frame. Our characterization relies on the connection between erasure optimal frames and the linear connectivity property of the frame. We prove that the linear connectivity property is equivalent to the intersection dependent property, and is also closely related to the well-known concept of ak-independent set. Additionally, we also establish several necessary and sufficient conditions for the existence of an alternate dual frame to make the iterative reconstruction work.