Adaptive discovery of sparse signals in noise

A multi-step adaptive resampling procedure is proposed, and shown to be an effective approach when detecting high-dimensional sparse signals in noise. Each step of the proposed procedure refines an estimate of the true signal subspace, allowing sensing energy to be focused more directly into the subspace of interest and significantly improving the performance of the final detection test. Large-sample analysis shows that for the sparse signal detection problems considered, the proposed adaptive sensing procedure outperforms the best possible detection methods based on non-adaptive sensing, allowing for the detection of signals that are exponentially weaker than what can be detected using non-adaptive samples.