Adaptive sensing of sparse signals and spectra

We consider multistage adaptive sensing of signals and spectra where the components of interest are sparse. The advantage of adaptation in this context is the ability to focus more of the sensing budget on regions where signal components exist, thereby improving the signal-to-noise ratio. A dynamic programming formulation is derived for the allocation of sensing resources to minimize the expected estimation loss. Based on the method of open-loop feedback control, tractable allocation policies are then developed for a variety of loss functions. The policies are optimal in the two-stage case and improve monotonically thereafter with the number of stages. We illustrate how our policies may be applied to radar imaging and to spectrum sensing, demonstrating dramatic gains compared to non-adaptive estimation and gains up to several dB compared to recently proposed adaptive methods.