We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High-dimensional testing problems in which it may be prohibitive or impossible to obtain a complete observation motivate this work. The signal is represented as a vector in ℝn, but we only observe m ≪ n of its elements.We show that reliable detection is possible, under mild incoherence conditions, as long as m is slightly greater than the dimension of the subspace in question.
展开▼
机译:我们考虑确定高度不完整的信号是否位于给定子空间中的问题。当完全观察到信号时,匹配子空间检测这个问题是经典的,经过充分研究的问题。高维测试问题(可能无法获得或无法获得完整的观察结果)推动了这项工作。信号用ℝ n sup>表示为矢量,但是我们仅观察到m≪ n个元素。我们证明,只要m略大于n,在温和的非相干条件下,可靠的检测是可能的。有关子空间的尺寸。
展开▼