论文标题
使用原子规范对结构化信号的统一恢复
A Unified Recovery of Structured Signals Using Atomic Norm
论文作者
论文摘要
在许多应用中，我们试图从线性测量值中恢复信号的少于环境维度，因为信号具有可剥削的结构，例如稀疏矢量或低级矩阵。在本文中，我们在一般环境中工作，该信号在所谓的原子集中大约稀疏。我们提供一般的恢复结果，指出，如果传感映射的空空间满足某些属性，则凸编程可以稳定，稳健地恢复信号。此外，我们认为，即使每个测量值是subgaussian，即使测量次数很少，这种空空间属性也可以很高的概率满足。结果也得出了一些新的结果，以恢复框架中稀疏的信号稀疏，并因此得出了恢复低级矩阵。
In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general setting where signals are approximately sparse in an so called atomic set. We provide general recovery results stating that a convex programming can stably and robustly recover signals if the null space of the sensing map satisfies certain properties. Moreover, we argue that such null space property can be satisfied with high probability if each measurement is subgaussian even when the number of measurements are very few. Some new results for recovering signals sparse in a frame, and recovering low rank matrices are also derived as a result.
