稀疏信号检测和支持度估计的自适应感知性能下界
Adaptive sensing performance lower bounds for sparse signal detection and support estimation
摘要：
本文给出了一个精确的表征的基本限制的自适应传感器的各种估计和测试问题的稀疏信号。我们认为，特别是在（IEEE Trans.通知。Theory 57（2011）6222-6235），并且示出了关于检测和估计两者的最小信号幅度的必要条件：如果${\mathbf {x}}\in \mathbb{R}^n$是具有$s$非零分量的稀疏向量，则如果非零分量的幅度超过$\sqrt{2/s}$，则可以在噪声中可靠地检测到它。此外，如果最小幅度超过$\sqrt{2\log s}$，则可以准确地识别信号支持。值得注意的是，不依赖于$n$，即外部信号维度。这些结果表明，以前在文献中提出的自适应传感方法基本上是最优的，不能大幅改善。此外，这些结果提供了对自适应压缩感知的限制的进一步见解。
英文摘要：
This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting introduced in (IEEE Trans. Inform. Theory 57 (2011) 6222-6235) and show necessary conditions on the minimum signal magnitude for both detection and estimation: if ${\mathbf {x}}\in \mathbb{R}^n$ is a sparse vector with $s$ non-zero components then it can be reliably detected in noise provided the magnitude of the non-zero components exceeds $\sqrt{2/s}$. Furthermore, the signal support can be exactly identified provided the minimum magnitude exceeds $\sqrt{2\log s}$. Notably there is no dependence on $n$, the extrinsic signal dimension. These results show that the adaptive sensing methodologies proposed previously in the literature are essentially optimal, and cannot be substantially improved. In addition, these results provide further insights on the limits of adaptive compressive sensing.
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