# 6.9 Compressive sensor networks

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This module provides an overview of applications of compressive sensing in the context of distributed sensor networks.

Sparse and compressible signals are present in many sensor network applications, such as environmental monitoring, signal field recording and vehicle surveillance. Compressive sensing (CS) has many properties that make it attractive in this settings, such as its low complexity sensing and compression, its universality and its graceful degradation. CS is robust to noise, and allows querying more nodes to obey further detail on signals as they become interesting. Packet drops also do not harm the network nearly as much as many other protocols, only providing a marginal loss for each measurement not obtained by the receiver. As the network becomes more congested, data can be scaled back smoothly.

Thus CS can enable the design of generic compressive sensors that perform random or incoherent projections.

Several methods for using CS in sensor networks have been proposed. Decentralized methods pass data throughout the network, from neighbor to neighbor, and allow the decoder to probe any subset of nodes. In contrast, centralized methods require all information to be transmitted to a centralized data center, but reduce either the amount of information that must be transmitted or the power required to do so. We briefly summarize each class below.

## Decentralized algorithms

Decentralized algorithms enable the calculation of compressive measurements at each sensor in the network, thus being useful for applications where monitoring agents traverse the network during operation.

## Randomized gossiping

In randomized gossiping  [link] , each sensor communicates $M$ random projection of its data sample to a random set of nodes, in each stage aggregating and forwarding the observations received to a new set of random nodes. In essence, a spatial dot product is being performed as each node collects and aggregates information, compiling a sum of the weighted samples to obtain $M$ CS measurements which becomes more accurate as more rounds of random gossiping occur. To recover the data, a basis that provides data sparsity (or at least compressibility) is required, as well as the random projections used. However, this information does not need to be known while the data is being passed.

The method can also be applied when each sensor observes a compressible signal. In this case, each sensor computes multiple random projections of the data and transmits them using randomized gossiping to the rest of the network. A potential drawback of this technique is the amount of storage required per sensor, as it could be considerable for large networks .In this case, each sensor can store the data from only a subset of the sensors, where each group of sensors of a certain size will be known to contain CS measurements for all the data in the network. To maintain a constant error as the network size grows, the number of transmissions becomes $\Theta \left(kM{n}^{2}\right)$ , where $k$ represents the number of groups in which the data is partitioned, $M$ is the number of values desired from each sensor and n are the number of nodes in the network. The results can be improved by using geographic gossiping algorithms  [link] .

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