Adaptive sensing performance lower bounds for sparse signal detection and support estimation

作者：Castro Rui M^*

来源：Bernoulli, 2014, 20(4): 2217-2246.

DOI：10.3150/13-BEJ555

• adaptive sensing
• minimax lower bounds
• sequential experimental design
• sparsity-based models

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 x is an element of 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 root 2/s. Furthermore, the signal support can be exactly identified provided the minimum magnitude exceeds root 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.

• 出版日期2014-11