论自适应传感的基本局限性
On the Fundamental Limits of Adaptive Sensing
摘要：
假设我们可以顺序地获取n维向量x的任意线性测量，从而得到线性模型y = Ax + z，其中z表示测量噪声。如果已知信号是稀疏的，那么人们会期望下面的民间定理是正确的：选择一种自适应策略，根据先前观察到的情况巧妙地选择A的下一行，应该比非自适应策略做得好得多，非自适应策略提前设置A的行，因此不试图在观察之间学习任何关于信号的信息。本文证明了民间定理是错误的。我们证明了聪明的自适应策略和复杂的估计程序-无论多么棘手-经典的压缩采集/恢复方案提供的优势是，在一般情况下，最小。
英文摘要：
Suppose we can sequentially acquire arbitrary linear measurements of an n-dimensional vector x resulting in the linear model y = Ax + z, where z represents measurement noise. If the signal is known to be sparse, one would expect the following folk theorem to be true: choosing an adaptive strategy which cleverly selects the next row of A based on what has been previously observed should do far better than a nonadaptive strategy which sets the rows of A ahead of time, thus not trying to learn anything about the signal in between observations. This paper shows that the folk theorem is false. We prove that the advantages offered by clever adaptive strategies and sophisticated estimation procedures---no matter how intractable---over classical compressed acquisition/recovery schemes are, in general, minimal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
