A Performance Guarantee for Adaptive Estimation of Sparse Signals

This paper studies adaptive sensing for estimating the nonzero amplitudes of a sparse signal. We consider a previously proposed optimal two-stage policy for allocating sensing resources. We derive an upper bound on the mean squared error resulting from the optimal two-stage policy and a corresponding lower bound on the improvement over non-adaptive sensing. It is shown that the adaptation gain is related to the detectability of nonzero signal components as characterized by a Bhattacharyya coefficient, thus quantifying analytically the dependence on the sparsity level of the signal, the signal-to-noise ratio, and the sensing resource budget. The bound is shown to be a good approximation to the optimal two-stage gain through numerical simulations.