Recently, it was discovered that for a given function class $\mathbf{F}$ the error of best linear recovery in the square norm can be bounded above by the Kolmogorov width of $\mathbf{F}$ in the uniform norm. That analysis is based on deep results in discretization of the square norm of functions from finite dimensional subspaces. In this paper we show how very recent results on universal discretization of the square norm of functions from a collection of finite dimensional subspaces lead to an inequality between optimal sparse recovery in the square norm and best sparse approximations in the uniform norm with respect to appropriate dictionaries.

翻译：最近发现，对于给定的函数类$\mathbf{F}$，在平方范数下最佳线性恢复的误差可由$\mathbf{F}$在一致范数下的柯尔莫哥洛夫宽度界定。该分析基于对有限维子空间函数平方范数离散化的深层研究成果。本文展示了针对有限维子空间集合中函数平方范数的通用离散化最新研究成果，如何导出平方范数下最优稀疏恢复与基于适当字典的一致范数下最佳稀疏逼近之间的不等式关系。