Multistage adaptive estimation of sparse signals

This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. A dynamic programming formulation is derived for the allocation of sensing resources to minimize a cost function related to mean squared estimation error. Allocation policies are developed based on the method of open-loop feedback control. These policies are optimal in the two-stage case and improve monotonically thereafter with the number of stages. Numerical simulations show gains up to several dB as compared to recently proposed adaptive methods, and dramatic gains approaching the oracle limit as compared to non-adaptive estimation.