论文标题
衍射极限的算法基础
Algorithmic Foundations for the Diffraction Limit
论文作者
论文摘要
一个半世纪以来，它被广泛认为（但从未严格表明），衍射物理学对光学系统的分辨率施加了一定的基本限制。但是，我们对确切和无法解决的问题的理解从未超过启发式论点，这些论点似乎甚至是矛盾的。在这项工作中，我们通过研究衍射极限作为统计反问题，并基于与可证明的学习混合模型的可证明的算法的联系来弥补这一差距，我们严格地证明了对解决较大间距点源所需的统计和算法复杂性的上限和下限。特别是我们表明，样品复杂性从多项式转变为指数。令人惊讶的是，我们表明这不是在ABBE限制下发生的，长期以来一直认为这是真正的衍射极限。
For more than a century and a half it has been widely-believed (but was never rigorously shown) that the physics of diffraction imposes certain fundamental limits on the resolution of an optical system. However our understanding of what exactly can and cannot be resolved has never risen above heuristic arguments which, even worse, appear contradictory. In this work we remedy this gap by studying the diffraction limit as a statistical inverse problem and, based on connections to provable algorithms for learning mixture models, we rigorously prove upper and lower bounds on the statistical and algorithmic complexity needed to resolve closely spaced point sources. In particular we show that there is a phase transition where the sample complexity goes from polynomial to exponential. Surprisingly, we show that this does not occur at the Abbe limit, which has long been presumed to be the true diffraction limit.
