There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling discretization results turn out to be very useful in various applications, particularly in sampling recovery. Recent sampling discretization results typically provide existence of good sampling points for discretization. In this paper, we show that independent and identically distributed random points provide good universal discretization with high probability. Furthermore, we demonstrate that a simple greedy algorithm based on those points that are good for universal discretization provides excellent sparse recovery results in the square norm.

翻译：在积分范数的采样离散化研究中，无论是针对指定的有限维函数空间还是有限个此类函数空间的集合（通用离散化），均已取得显著进展。采样离散化结果在众多应用中极为有用，尤其在采样恢复领域。近期采样离散化研究成果通常证明了存在良好的采样点以实现离散化。本文表明，独立同分布的随机点能以高概率实现良好的通用离散化。此外，我们证明基于这些适用于通用离散化的点所构建的简单贪婪算法，在平方范数下可获得优异的稀疏恢复结果。