论文标题
关于线性反问题中多面体估计的设计
On Design of Polyhedral Estimates in Linear Inverse Problems
论文作者
论文摘要
在观测值的常规中，多面体估计是一种通用的有效计算的非线性，用于恢复属于信号线性图像的嘈杂观察到给定凸的紧凑型的未知信号。风险分析和多面体估计的最佳设计可以通过有效地界定优化问题的最佳值来解决。这些问题通常很难；然而，在Nemirovski 2019年的Juditsky显示，当信号集是一个椭圆形时，可以有效地构建最佳最佳（“达到对数因素”）估计值 - 凸出和紧凑型几何集的一家特殊几何集的成员（请参阅E.G.，Juditsky，Nemirovski 2018）。本文的主题是在信号集是椭圆形的相交和任意多层的情况下，对多面体估计的新风险分析，允许在这种情况下改善多面体估计设计。
Polyhedral estimate is a generic efficiently computable nonlinear in observations routine for recovering unknown signal belonging to a given convex compact set from noisy observation of signal's linear image. Risk analysis and optimal design of polyhedral estimates may be addressed through efficient bounding of optimal values of optimization problems. Such problems are typically hard; yet, it was shown in Juditsky, Nemirovski 2019 that nearly minimax optimal ("up to logarithmic factors") estimates can be efficiently constructed when the signal set is an ellitope - a member of a wide family of convex and compact sets of special geometry (see, e.g., Juditsky, Nemirovski 2018). The subject of this paper is a new risk analysis for polyhedral estimate in the situation where the signal set is an intersection of an ellitope and an arbitrary polytope allowing for improved polyhedral estimate design in this situation.
