A new probabilistic model for optimal frames in erasure's recovery

Signal recovery and frames that are robust to erasure

We consider finite frames with high redundancy so that if half the terms transmitted from the sender are randomly deleted during transmission, then on average, the receiver can still recover the signal to within a high level of accuracy. This follows from a result in random matrix theory. We also give an application of the operator Khintchine inequality in the setting of signal recovery when the signal is a matrix with a sparse representation.

Hilbert-Schmidt范数下概率擦除的最优对偶框架结构

The structure of optimal dual frames for probabilistic erasures under Hilbert--Schmidt norm

本文研究Hilbert-Schmidt范数下概率擦除的最优对偶框架，刻画1-擦除最优对偶框架，给出规范对偶最优且唯一的条件，推导m-擦除概率重构误差下界，并分析最优对偶框架集的几何结构。

关于论文《概率擦除的最优对偶框架》

On the paper Optimal dual frames of probabilistic erasures

本文通过反例指出原论文关于1次擦除重构唯一概率最优对偶的条件不充分且证明有误，修正了定理并指出紧框架假设下唯一性推论错误，完善了相关理论刻画。

Matrix Methods for Perfect Signal Recovery Underlying Range Space of Operators

The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical K-dual. % and survey optimal K-dual problem under probabilistic erasures. Then, we survey the problem of recovering and robustness of signals when the erasure set satisfies the minimal redundancy condition or the K-frame is maximal robust. Furthermore, we show that the error rate is reduced under erasures if the $K$-frame is of uniform excess. Toward the prote…

Probabilistic Modelled Optimal Frame for Erasures under Spectral and Operator Norm

Error occurs in data transmission process when some data are missing at the time of reconstruction. Finding the best dual frame or a dual pair that minimizes the reconstruction error when erasure occurs,is a deep-rooted problem in frame theory. The main motivation behind this paper is to characterize the optimal dual under the spectral and operator norms. Here we give several equivalent conditions for which the canonical dual is an optimal dual frame for a given frame. We also go on to characterize the set of dual pairs which attains the optimal value.

存在擦除时的最优K对偶框架与最优K对偶对

Optimal K dual frames and pairs in the presence of erasures

该研究针对框架系数传输中的擦除问题，探究K-框架的最优K-对偶框架与对偶对结构，分析两类擦除场景的影响，以最小化误差算子谱半径和算子范数为最优准则，构建了缓解擦除效应的框架，提升数据传输恢复鲁棒性。