## 6 Simulation Results
### Energy Consumption Evaluation  
To illustrate the efficiency of our proposed data-gathering technique, we compare the results obtained from the non-CS, plain CS, and hybrid CS data-gathering schemes for data to the sink node using \(Dijkstra\) algorithm and our proposed algorithm, where measurement \(M\in[30~{}220]\) and the frame length of data is 750. The number of sensor nodes is 80. From Figure 15, it can be seen that non-CS consumes the most energy, about \(3.91~{}\times~{}10^{3}\) J, and the value is unchanged as the number of CS measurements steadily increases because the scheme does not adopt the CS technique. In addition, hybrid CS consumes about \(1.22~{}\times~{}10^{3}\) J compared with \(1.51\times 10^{3}\) J for plain CS when the number of CS measurements is 50. Both display an upward trend with the rise in the number of CS measurements, but the energy consumption of hybrid CS is always less than that of plain CS. The difference is about \(0.46~{}\times~{}10^{3}\) J when the number of CS measurements is at its maximum, 220. The reason is that the hybrid CS scheme uses the CS mechanism or not based on the number of transmission packets. Therefore, hybrid CS takes advantage of non-CS and plain CS to reduce the energy consumption of the network. However, the data-gathering scheme using the \(Dijkstra\) algorithm consumes less energy than hybrid CS because the former makes full use of our modified diffusion wavelets and sparse random matrix. When the number of measurements is about 110, the gap between hybrid CS and \(Dijkstra\) reaches a maximum; when the number of CS measurements is 220, the difference is minimal. Our proposed data-gathering scheme using diffusion wavelets based on distance and a modified ant colony algorithm shows better performance compared with other methods. It is obvious that it considers a sensor node's distance to exploit spatial correlation and sensor nodes' residual energy and path length are jointly taken into consideration. Thus, the scheme consumes less energy. When the number of CS measurements achieves the maximum (220), the advantage of this approach is more prominent: the transmission cost is about \(2.18\times 10^{3}\) J. This is far less than for the other four schemes in terms of energy consumption. From Figures 14 and 15, we can observe that although the recovery error has become smaller, the transmission cost has increased a lot. Therefore, there is a trade-off between energy consumption and recovery error.  
Moreover, to further evaluate the performance of the proposed algorithm, Figure 16 is plotted, where energy consumption comparisons are shown among different data-gathering schemes with a change in the number of sensor nodes. It can be seen from Figure 16 that the non-CS technique always consumes the most energy as the number of sensor nodes increases from 100 to 800 because it does not use any compressive methods. However, plain CS dramatically reduces the network energy consumption compared with the non-CS. The reason is that it takes advantage of compressive sensing. Obviously, the energy consumption of hybrid CS decreases compared with plain CS. The number of sensor nodes is fewer than 400 and the difference between plain CS and hybrid CS is small; when the number of sensor nodes is 800, the gap between plain CS and hybrid CS is largest. That is to say, the energy efficiency of hybrid CS is more significant with an increase in the number of sensor nodes. Additionally, the transmission costs of the \(Dijkstra\) algorithm are lowered because of the sparse measurement matrix, as is shown in Figure 16. The performance of our proposed algorithm is better than all of the abovementioned schemes. Especially when the number of sensor nodes is greater than 500, the performance of our algorithm is more significant. This is why sparse represent basis is used and our improved ant colony algorithm is presented in the process of data gathering.