# Design of Robust Sensing Matrix for UAV Images Encryption and Compression
## 4 Experiment
_Case 2: The recovery of test images from UAV123 datasets with different dimensions of the sensing matrix._ In this case, eleven UAV images (Figure 2) are selected randomly from eleven classifications (\"bike\", \"bird\", \"boat\", \"building\", \"car\", \"group\", \"person\", \"truck\", \"wakeboard\", \"game\" of size \(1280\times 720\), and \"uav\" of size \(720\times 480\)), respectively. These UAV images are compressed by five sensing matrices with different dimensions of \(M=20\) and \(M=24\), which achieve the recovery performance of PSNRs, SREs and SSIMs. In addition, the results of those evaluation indexes between the recovery images and the original images are also listed in Table 2.  
**Remark 2**. :
* Considering the SRE, a more robust sensing matrix can be designed, which leads to better recovery performance by using algorithm \(CS_{LLL}\), algorithm \(CS_{HZ}\) and algorithm \(CS_{LESM}\). The experimental results are matched with the above theoretical analysis. * According to the previous theoretical analysis, the PSNR of algorithm \(CS_{HZ}\) is worse than algorithm \(CS_{LLL}\). However, algorithm \(CS_{HZ}\) possesses the lower computational complexity. * In terms of algorithms \(CS_{LLL}\) and \(CS_{LESM}\), they both consider the influence of SRE, which is calculated from the training samples directly. However, for the algorithm \(CS_{LLL}\), the SRE is achieved by eliminating one group of sparse representation, while for the algorithm \(CS_{LESM}\), the LSRE is achieved by eliminating several groups of sparse representation. The result of the experiments is listed in Table 2, where the PSNRs and SSIMs of algorithm \(CS_{LESM}\) are higher than those of algorithm \(CS_{LLL}\). The algorithm \(CS_{LESM}\) decreases the SRE to achieve the true error. * In terms of PSNR and SSIM, the algorithm \(CS_{LESM}\) obtains the highest recovery performance for each kind of image from the UAV123 datasets. In addition, the SREs of algorithm \(CS_{LESM}\) are also the lowest. * For different compression ration \(M/64\) with \(M=20\) and \(M=24\), algorithm \(CS_{LESM}\) achieves the best recovery performance. The PSNRs, SREs, and SSIMs for the higher compression ration (\(M=24\)) are better than the lower one for most of the sensing matrix, especially for algorithm \(CS_{LESM}\). _Case 3: Recovery test on images from UAV123 datasets with a different noise._ In this case, we simulate the scenario where the images are taken by the UAV when the UAV is interfered with by flight stability and a harsh environment. Eleven UAV images (Figure 2) are added with different levels of Gaussian noise, respectively. These noisy UAV images are compressed by five sensing matrices with different noises of \(SNR\) = 20 dB, \(SNR\) = 30 dB \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & \(\|\mathbf{I_{L}-G}\|_{\text{F}}^{2}\) & \(\|\mathbf{\Phi\Delta E}\|_{\text{F}}^{2}\) & \(\mathbf{\mu_{av}(D)}\) & \(\mathbf{\mu(D)}\) \\ \hline \(CS_{RAN}\) & \(6.8\times 10^{5}\) & \(5.68\times 10^{3}\) & 0.4124 & 0.9874 \\ \hline \(CS_{LZY}\) & 80.0000 & 53.9172 & 0.3553 & 0.9359 \\ \hline \(CS_{LLL}\) & 83.1286 & 22.1217 & 0.3639 & 0.9384 \\ \hline \(CS_{HZ}\) & 80.3562 & 43.9250 & 0.3571 & 0.9387 \\ \hline \(CS_{LESM}\) & **82.2070** & **0.4838** & **0.3609** & **0.9443** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance evaluated with five sensing matrices. and no noise (\(SNR=\infty\)), which achieve the recovery performance of PSNRs, SREs and SSIMs listed in Table 3.
* The algorithm \(CS_{LESM}\) achieves the best recovery performance in every noise level. In addition, the larger noise the image contains, the more obvious the improvement space of the recovery results are. We analyzed the statistical data \"average\" obtained from eleven images, and the enhancement of the PSNRs value between the best algorithm \(CS_{LESM}\) and the second best one is 0.44 dB when the noise \(SNR=\) 20 dB, 0.25 dB when the noise \(SNR=\) 30 dB and 0.21 dB when no noise \(SNR=\infty\).