Adaptive sequential compressive detection

Sparsity is at the heart of numerous applications dealing with multidimensional phenomena with low-information content. The primary question that this work investigates is whether, and how much, further compressive gains could be achieved if the goal of the inference task does not require exact reconstruction of the underlying signal. In particular, if the goal is to detect the existence of a sparse signal in noise, it is shown that the number of measurements can be reduced. In contrast to prior work, which considered non-adaptive strategies, a sequential adaptive approach for compressed signal detection is proposed. The key insight is that the decision can be made as soon as a stopping criterion is met during sequential reconstructions. Two sources of performance gains are studied, namely, compressive gains due to adaptation, and computational gains via recursive sparse reconstruction algorithms that fuse newly acquired measurements and previous signal estimates.