论文标题
有限的Riesz系统中的稀疏恢复，并应用于PDE的数值方法
Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs
论文作者
论文摘要
我们研究具有独立，相同分布和统一的行以及非平凡协方差结构的结构化随机测量矩阵的稀疏恢复。这类矩阵来自有界Riesz系统的随机采样，并概括了随机的部分傅立叶矩阵。我们的主要结果改善了此类随机矩阵的无效空间和限制等轴测特性的当前可用结果。我们分析的主要新颖性是一种新的上限，以期望与限制等轴测常数相关的Bernoulli过程的上限。我们应用结果来证明Corsing方法的新绩效保证，这是一种基于压缩感应的最近引入的针对部分微分方程（PDE）的数值近似技术。
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of bounded Riesz systems and generalizes random partial Fourier matrices. Our main result improves the currently available results for the null space and restricted isometry properties of such random matrices. The main novelty of our analysis is a new upper bound for the expectation of the supremum of a Bernoulli process associated with a restricted isometry constant. We apply our result to prove new performance guarantees for the CORSING method, a recently introduced numerical approximation technique for partial differential equations (PDEs) based on compressive sensing.
