Compressive sensing (CS)-based data gathering is a promising method to reduce energy consumption in wireless sensor networks (WSNs). Traditional CS-based data-gathering approaches require a large number of sensor nodes to participate in each CS measurement task, resulting in high energy consumption, and do not guarantee load balance. In this paper, we propose a sparser analysis that depends on modified diffusion wavelets, which exploit sensor readings’ spatial correlation in WSNs. In particular, a novel data-gathering scheme with joint routing and CS is presented. A modified ant colony algorithm is adopted, where next hop node selection takes a node’s residual energy and path length into consideration simultaneously. Moreover, in order to speed up the coverage rate and avoid the local optimal of the algorithm, an improved pheromone impact factor is put forward. More importantly, theoretical proof is given that the equivalent sensing matrix generated can satisfy the restricted isometric property (RIP). The simulation results demonstrate that the modified diffusion wavelets’ sparsity affects the sensor signal and has better reconstruction performance than DFT. Furthermore, our data gathering with joint routing and CS can dramatically reduce the energy consumption of WSNs, balance the load, and prolong the network lifetime in comparison to state-of-the-art CS-based methods.

One of the major concerns in 5G IoT networks is that most of the sensor nodes are powered through limited lifetime, which seriously affects the performance of the networks. In this article, Compressive sensing (CS) technique is used to decrease transmission cost in 5G IoT networks. Sparse basis is one of the important steps in the CS. However, most of the existing sparse basis-based method such as DCT (Discrete cosine transform) and DFT (Discrete Fourier Transform) basis do not capture data structure characteristics in the networks. They also do not take into consideration multi-resolution representations. In addition, some of sparse basis-driven methods exploit either spatial or temporal features, resulting in performance degradation of CS-based strategies. To address these challenging problems, we propose a novel spatial–temporal correlation basis algorithm (SCBA). Subsequently, an optimal basis algorithm (OBA) is provided considering greedy scoring criteria. To evaluate the efficiency of OBA, orthogonal wavelet basis algorithm (OWBA) by employing NS (Numerical Sparsity) and GI (Gini Index) sparse metrics is also presented. In addition, we discuss the complexity of the above three algorithms, and prove that OBA has low numerical rank. After experimental evaluation, we found that OBA is capable of the sparsest representing original signal compared to spatial, DCT, haar-1, haar-2, and rbio5.5. Furthermore, OBA has the low recovery error and the highest efficiency.