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.

我们使用结构随机测量矩阵研究稀疏恢复，该结构具有独立，均匀分布和均匀有界的行，并且具有非平凡的协方差结构。此类矩阵来自有界Riesz系统的随机采样，并且推广了随机的部分傅立叶矩阵。我们的主要结果改进了此类随机矩阵的零空间和受限等距特性的当前可用结果。我们的分析的主要新颖之处是期望与受限等轴测常数相关联的伯努利过程的最大值的新上限。我们应用我们的结果来证明CORSING方法的新性能保证，CORSING方法是最近引入的基于压缩传感的偏微分方程（PDE）数值近似技术。