## 2 Related Work  
Recently, numerous CS-based data-gathering approaches have been provided to increase the network's lifetime by decreasing the amount of transmission data and balancing load of the whole WSNs [12; 13; 20; 21]. [PERSON] et al. first analyzed the CS-based data-gathering scheme (plain CS) in large-scale WSNs, namely, compressive data gathering (CDG) [12]. In [12], [PERSON] et al. prove that the network capacity is proportional to the sparsity level of sensor node readings. However, this method also demonstrates that an increase in the number of measured samples leads to growth of transmission costs compared to the non-CS approach. CStorage [13] exploits the spatial correlation of sensor node readings along with CS to reduce the number of transmission data points, aiming at prolonging the WSNs' lifetime. [PERSON] et al. introduce compressive wireless sensing, whereby a distributed, matched-source channel communication architecture was proposed for energy-efficient estimation of sensor node readings [20]. However, sensor node readings' spatial correlation features in [20] are not considered. The authors of [21] show that hybrid CS can achieve high network throughput, while plain CS may not yield a significant improvement in throughput because of the dense measurement matrix. Up to now, the interaction between routing and compression data gathering has seriously hindered the progress of CS in WSNs [12; 22]. These data-gathering methods jointly use routing and CS to mitigate the data throughput. The authors of [22] address the data collection problem in WSNs, with routing used in combination with CS to transmit random data projections. However, this technique demonstrates that a sparse measurement matrix not only deviates from RIP property, but does not minimize transport energy consumption for each CS measurement. Nevertheless, in [12], [PERSON] et al. claim that measurement matrix [I R] has good RIP; in addition, CDG can further reduce communication costs for both chain-type and tree-type routing. Alternatively, this method requires a large number of sensor nodes involved in each projection gathering, bringing about high transmission costs. To significantly reduce data traffic and save power, distributed multi-chain compressive sensing based on a routing algorithm in WSNs is presented. However, the measurement matrix is still a dense measurement matrix [16]. In [23], a distributed sparse random measurement is proposed, where the sparse or compressible signal can be recovered. [PERSON] et al. consider that some sensor nodes instead of all of them are required in each measurement. Furthermore, the authors of [23] show that sparse random projection significantly enhances network performance. The communication costs can be reduced to \(O(\log N)\) packets per sensor, but this strategy utilizes random routing in the networks, which mitigates the energy efficiency of WSNs. In [14] a sparest random scheduling for compressive data gathering in WSNs is provided to satisfy RIP property; a sparse basis is designed based on the measurement matrix and sensor node readings. The scheme claims that it can achieve good results in real datasets, but the routing is not considered. Routing and CS are also incorporated into [17], which considers special random routing of a given network topology. However, sensor nodes' compressible ration and routing schemes considerably affect the transport costs. In fact, this method is impractical since sensor nodes are randomly deployed in the field of WSNs applications. In [18], [PERSON] et al. introduces an algorithm based on a random walk that is independent of network topology. Nevertheless, those techniques in [14; 17; 18; 23] suffer from the fact that the routing of the projection to the sink node is not optimal, which leads to an extra transmission bottleneck for the sensor nodes near the sink node in WSNs. [19] follows the dense matrix used in [12] and hybrid CS in [21]; a cluster-based data-gathering scheme is proposed.