论文标题
矩阵方法的完美信号恢复的基础运算符的范围范围
Matrix Methods for Perfect Signal Recovery Underlying Range Space of Operators
论文作者
论文摘要
本文的最重要目的是通过矩阵方法研究有限维的希尔伯特空间，在有限的维度希尔伯特空间中研究了完美的重建范围。为此，首先，我们获得了更多规范k二的结构。 ％和调查在概率擦除下的最佳K二重问题。然后，我们调查当擦除集满足最小冗余条件或K框架最大的稳健性时，我们调查了信号恢复和鲁棒性的问题。此外，我们表明，如果$ k $ frame的超额均匀，则在擦除下降低了错误率。为了保护编码框架（k-dual）免受擦除，我们引入了一个称为$（r，k）$矩阵的新概念，以恢复丢失的数据并通过矩阵方程解决完美的恢复问题。此外，我们通过使用最小的冗余条件在运算符的解码框架上使用最小的冗余条件来讨论此类矩阵的存在。最后，我们展示了几个示例，这些示例说明了我们的结果以及使用新矩阵在存在和构造的先前方法方面的优势。
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 protection of encoding frame (K-dual) against erasures, we introduce a new concept so called $(r,k)$-matrix to recover lost data and solve the perfect recovery problem via matrix equations. Moreover, we discuss the existence of such matrices by using minimal redundancy condition on decoding frames for operators. Finally, we exhibit several examples that illustrate our results and the advantage of using the new matrix with respect to previous approaches in existence and construction.
