## 5 Simulation and Discussion
### Reconstruction Performances under Different Temporal Compression Ratios  
Based on the imaging principle of CACTI, the compression ratio, coded matrix, and motion feature affect the results significantly. The coded matrix and motion features are restricted by the hardware system and observation scene. The compression ratio is relevant to the stepping precision of the motion controller of the active coded element and the pixel size of the detector, which is the main specification of CACTI. The simulation results of the proposed multi-regularization algorithm compared with other algorithms are shown in Figures 5 and 6. There are two videos synthesized for reconstruction. These synthetic videos differ in their features. The traffic video is dominated by a moving foreground, but the eye-blink video has more of a fixed background. The traffic video contains multiple moving objects, while the eyeblink video only contains one moving object. Figure 5: Reconstructed frames 14 for the eye blink dataset by multi-regularization algorithms for comparison: (**a**) ground truth; (**b**) result constructed by GAP-acc + TV algorithm; (**c**) result constructed by GAP + b algorithm; (**d**) result constructed by proposed multi-regularization algorithm; (**e**) the residual images of (**b**); (**f**) the residual images of (**c**); (**f**) the residual images of (**d**). Figure 6: Reconstructed frame 8 for the traffic dataset by multi-regularization algorithms for comparison: (**a**) frame reconstructed by GAP-acc + TV algorithm with \(N_{f}=8\); (**b**) frame reconstructed by GAP + b algorithm with \(N_{f}=8\); (**c**) frame reconstructed by proposed algorithm with \(N_{f}=8\); (**d**) frame reconstructed by GAP-acc + TV algorithm with \(N_{f}=24\); (**e**) frame reconstructed by GAP + b algorithm with \(N_{f}=24\); (**f**) frame reconstructed by proposed algorithm with \(N_{f}=24\); (**g**) the residual images of (**a**); (**h**) the residual images of (**b**); (**i**) the residual images of (**c**); (**j**) the residual images of (**d**); (**k**) the residual images of (**e**); (**l**) the residual images of (**f**). High-speed video of an eye blink, from closing to opening, is reconstructed from a single coded snapshot for \(N_{F}=14\). It is noticeable that the eye is the only part of the scene that moves. There is little aesthetic difference between these reconstructions. Reconstructed results using multi-regularization algorithm and residual for the traffic dataset are shown in Figure 6. Frames reconstructed with GAP + b look better in the background but exhibit ghosting effects in the foreground due to ambiguities in the solution. The GAP-acc + TV can generally reconstruct the frames with sharper scenes than GAP + b but exhibits information loss and over-smoothness of reconstructed results. Compared with other algorithms, the proposed multi-regularization algorithm can provide richer texture information and sharper structure both in the background and foreground. When \(N_{f}=24\), the reconstructed result drops significantly, but the proposed multi-regularization algorithm can still identify the target in the scene. Visual quality evaluations on the reconstructed frames are consistent with the peak-to-peak signal-to-noise ratio (PSNR) results and residual images shown in Figure 7.  
Figure 7 plots the PSNR curves and reconstruction error curves against the frame for comparison of the algorithms with the traffic dataset under the temporal compression ratio from 4 to 48 frames with a single coded snapshot. The performance of all algorithms drops significantly when the compression ratio is larger than 24. As shown in Figure 6d-f, the reconstructed frame cannot be useful to target recognition. Therefore, the proposed multi-regularization algorithm becomes the better choice in terms of balancing reconstruction quality and robustness. The performance of GAP + b drops significantly when the compression ratio grows.