# A Chaotic Compressive Sensing Based Data Transmission Method for Sensors within BBNs
## 9 Conclusions  
In this paper, we propose a secure and efficient BBN data transmission method that could accomplish critical information concealment and retrieval. Generally, BBN sensors are resource constrained, and CS-based methods are naturally suitable for these sensors, as CS can accomplish data compression while sampling, and this process just needs simple operations of addition and multiplication, which could achieve the aim of reducing energy consumption of sensors during data processing and transmitting. The experimental results show that the proposed methods could compress and encrypt the original data and render different reconstruction results to users in different authorization groups. Namely, users in restricted-authorized groups could only obtain reconstruction results with critical sectors concealed, whereas users in full-authorized groups could reconstruct entire data.  
Moreover, in the proposed method, chaotic systems are introduced to generate measurement matrices, so the senders and receivers do not need to transmit the entire measurement matrices to one another, which further saves transmission energy. Specifically, the proposed method could enhance the security level of data transmission by breaking the statistical patterns of original data, providing large key space and sensitivity of the initial values, etc. The key space of the proposed method is discussed, and simulation results show that when even a slight change is applied to the initial value of the chaotic sequences, 10-15 to 10-17, for example, the experimental reconstruction results greatly change.  
Last but not least, experimental results also show that the proposed method enables the senders to conceal critical information with flexibility in terms of proportions and quantities of the concealed sectors. In summary, the proposed method realizes the protection of critical information that may be transmitted within BBNs. In the future, the combination of information concealment and semi-tensor compressive sensing could be studied, in order to enhance efficiency and flexibility levels of data transmission catering to the coming requirements of appliances in BBNs and even in IoT.  
Conceptualization, H.P. and W.W.; methodology, W.W. and H.P.; software, W.W., H.P. and B.X.; validation, W.W., H.P., F.T., L.L. and B.X.; formal analysis, W.W., F.T., B.X. and L.L.; writing--original draft preparation, W.W. and H.P.; writing--review and editing, L.L., F.T. and B.X. All authors have read and agreed to the published version of the manuscript. Please see the CRediT taxonomy for the term explanation.  
This research was funded in part by the National Key Research and Development Program of China (Grant no. 2020 YFB1805402), the National Natural Science Foundation of China (Grant nos. 61972051, 62032002), BUPT Excellent Ph.D. Students Foundation (CX2022139), the Natural Science Foundation of Beijing Municipality (Grant no. M21034), the 111 Project (Grant no. B21049) and the Young innovation team of colleges and universities in Shandong province (2021 KJ001).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Compression Rate 0.5**} \\ \hline
**Image** & \
\begin{tabular}{c} **Proposed** \\ **Method** \\ \end{tabular} & **Ref. [48]** & **Ref. [49]** & **Ref. [50]** \\ \hline lena & 25.79 & 29.82 & 29.82 & - \\ cameraman & 22.91 & 26.71 & 29.43 & - \\ peppers & 26.03 & - & - & 24.85 \\ woman & 31.16 & - & - & 30.82 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c} \hline
**Image** &
\begin{tabular}{c} **Proposed** \\ **Method** \\ \end{tabular} & **Ref. [48]** & **Ref. [49]** & **Ref. [50]** \\ \hline lena & 13.95 & 25.93 & 26.06 & - \\ cameraman & 15.07 & 22.64 & 25.23 & - \\ peppers & 17.80 & - & - & 19.16 \\ woman & 17.47 & - & - & 25.05 \\ \hline \hline \end{tabular}
\end{table}
Table 10: _Cont._