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 non-adaptive sensing would fail dramatically. In this work 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: (i) mitigate the effect of observation noise when compared to non-adaptive sensing and, (ii) capitalize on structural information to a much larger extent than possible with non-adaptive 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.

e‐LiteSense: Self‐adaptive energy‐aware data sensing in WSN environments

“…Indeed, the complex relation between data analysis and data acquisition in adaptive sensing paradigms can be highly powerful, as it allows a reliable estimation in situations where non‐adaptive sensing fails . Castro and Tanczos present a general estimation procedure which may be satisfactory for a variety of cases; however, it is recognised that requiring prior knowledge of some parameters might not be available in a real life setting.…”

Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets

“…Remark 1. As mentioned in the introduction, this work can be seen as an extension of [18] from component-wise sampling to the more general compressive sensing, and it is instructive to briefly discuss the differences between the two setups. Component-wise observations can be viewed as restricting compressive sensing by requiring each measurement vector A i to have exactly one non-zero entry (though the problem is set up a bit differently in [18] the two are effectively the same).…”

“…The authors of [18] also consider the problem of recovering structured supports using coordinate-wise observations, but in a setting where these are collected in a sequential and adaptive manner. Therefore this paper can be seen as an extension of [18] in that we move from coordinate-wise observations to compressed sensing. Although some of the techniques and insights can be used from that work, changing the measurement model introduces a number of new challenges to tackle.…”

“…This means that structural information is captured in the observations in a different way, which influences both the theoretical limits and the way support recovery procedures need to be designed. For a more extensive literature review in the setting of coordinate-wise observations we also direct the reader to [18].…”

Lightweight Multivariate Sensing in WSNs

“…The complex relation between analysis and data acquiring in adaptive sensing paradigms can be extremely powerful, as many times it allows a reliable estimation and signal detection in situations where non-adaptive detection fails [6]. For this reason, the authors investigate a general signal estimation over the adaptive detection paradigm problem, however, they also recognize that the prior knowledge of some required parameters might not be available in a real-life setting.…”