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On the Fundamental Limits of Adaptive Sensing

机译：自适应传感的基本极限

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摘要

Suppose we can sequentially acquire arbitrary linear measurements of an $n$ -dimensional vector ${bf x}$ resulting in the linear model ${bf y}= {bf A} {bf x} + {bf z}$, where ${bf z}$ 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 ${bf A}$ based on what has been previously observed should do far better than a nonadaptive strategy which sets the rows of ${bf A}$ 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.
机译：假设我们可以依次获取$ n $维矢量$ {bf x} $的任意线性测量结果，得到线性模型$ {bf y} = {bf A} {bf x} + {bf z} $，其中{bf z} $表示测量噪声。如果已知信号稀疏，则可以预期以下民间定理是正确的：选择一种自适应策略，该策略根据先前观察到的结果巧妙地选择$ {bf A} $的下一行，其效果远胜于a非自适应策略，它会提前设置$ {bf A} $的行，因此不会尝试在两次观察之间学习有关信号的任何信息。本文证明了民间定理是错误的。我们证明，与经典的压缩采集/恢复方案相比，无论多么难处理，聪明的自适应策略和复杂的估计程序所提供的优势通常是最小的。

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