论文标题
概率模拟了平均的频谱最佳双帧和双对，以擦除
Probability Modelled Averaged Spectrally Optimal Dual Frame and Dual Pair for Erasure
论文作者
论文摘要
从框架理论的角度来看，找到最佳的双帧和最佳双对以进行信号重建，这可以在数据传输过程中擦除时最小化重建误差，这是一个深根的问题。在本文中，我们通过使用概率擦除的频谱半径和操作员规范的平均值来考虑对错误操作员的新测量。在此测量中，最佳的双帧称为概率平均频谱最佳双帧，简短和最佳双对中的pasod框架称为pasod-pair。已经研究了预选框架的Pasod-Frames集合的属性。我们证明所有pasod框架的集合都是凸，封闭和紧凑的。我们还表明，在任何统一操作员下，pasod框架和pasodpair的图像也是pasod-frame和pasodpair。我们为特定框架$ f的唯一pasod框架提供了几种等效条件。此外，在给定框架的某些条件下，我们证明了pasod-Frame的唯一性。我们还继续表征所有pasod对的集合，并为双对成为POD，PSOD和PASOD-PAIR提供了几种等效条件。
Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep rooted problem from the perspective of frame theory. In this paper, we consider a new measurement for the error operator by taking the average of spectral radius and operator norm with probabilistic erasure. In this measurement, optimal dual frames are called Probabilistic Averaged Spectrally Optimal Dual frames, PASOD-frames in short and optimal dual pair is called PASOD-pair. The properties of the set of PASOD-frames for a pre-selected frame, has been studied. We prove that the set of all PASOD-frames is convex, closed and compact. We also show that the image of a PASOD-frame and PASOD-pair under any unitary operator is also a PASOD-frame and PASOD-pair. We provide several equivalent conditions for the canonical dual to be the unique PASOD-frame for a given frame $F.$ Moreover, we prove non-uniqueness of PASOD-frame under certain condition of the given frame. We also go on to characterize the set of all PASOD-pairs and give several equivalent conditions for a dual pair to become POD, PSOD and PASOD-pair.
