Multistage Adaptive Estimation of Sparse Signals

This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal components exist, thereby improving performance. A dynamic programming formulation is derived for the allocation of sensing effort to minimize the expected estimation loss. Based on the method of open-loop feedback control, allocation policies are then developed for a variety of loss functions. The policies are optimal in the two-stage case, generalizing an optimal two-stage policy proposed by Bashan et al., 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 compared to non-adaptive estimation. An application to radar imaging is also presented.