Adaptive Sensing for Estimation of Structured Sparse Signals

Abstract

In many practical settings one can sequentially and adaptively guide the collection of future data, based on information extracted from data collected previously. These sequential data collection procedures are known by different names, such as sequential experimental design, active learning, or adaptive sensing/sampling. The intricate relation between data analysis and acquisition in adaptive sensing paradigms can be extremely powerful, and often allows for reliable signal estimation and detection in situations where nonadaptive sensing would fail dramatically. In this paper, we investigate the problem of estimating the support of a structured sparse signal from coordinate-wise observations under the adaptive sensing paradigm. We present a general procedure for support set estimation that is optimal in a variety of cases and shows that through the use of adaptive sensing one can: 1) mitigate the effect of observation noise when compared with nonadaptive sensing and 2) capitalize on structural information to a much larger extent than possible with nonadaptive sensing. In addition to a general procedure to perform adaptive sensing in structured settings, we present both performance upper bounds, and corresponding lower bounds for both sensing paradigms.