## 5 Simulation and Discussion
### Performance of Spatiotemporal Super-Resolution Reconstruction  
According to the comparison and analysis in Section 5.2, for the given noise conditions and compression ratios, the current reconstruction algorithms cannot significantly improve the quality of reconstructed images. Therefore, more consideration is drawn on the inter-frame non-redundant information of the reconstructed image sequences. In this section, we conduct simulations to verify the effectiveness of the MAP-MRF-based SR approach for CACTI. We compare performances of the GAP + b algorithm, the Gap-acc + TV algorithm, the proposed multiple regularization reconstruction algorithm, and the 3D Steering Kernel Regression algorithm which is classical spatiotemporal super resolution algorithms. For detailed comparison, one arbitrarily selected frame from each of the reconstructed SR sequences is shown in Figure 12. It should be noted that our result is an improvement of the time and spatial resolution simultaneously, and the results were scaled to facilitate the comparison to others. The estimation results of different algorithms are used as the initial input of the LR sequence, and the output results reconstructed by MAP-MRF-based approach can reflect the error propagation. As shown in Figure 12i,j, both GAP + b algorithm and GAP-acc + b algorithms cause the error propagation, especially at the edge of the motion target. In the proposed MAP-MRF approach, the multi-regularization algorithm and coarse-to-fine scheme can address error propagation and significantly improve the performance. Figure 11: Performance comparison of CACTI reconstructive algorithms under noise conditions (variances = 0.05): (**a**) PSNR for reconstructed frames of Traffic with \(N_{f}=8\); (**b**) PSNR for reconstructed frames of Traffic with \(N_{f}=22\); (**c**) reconstruction error for reconstructed frames of Traffic with \(N_{f}=8\); (**d**) reconstruction error for reconstructed frames of Traffic with \(N_{f}=22\). Figure 12: _Cont._  
Some close-ups of the reconstructed results are enlarged and presented below the corresponding frames. As proven in Figure 13, the approach proposed herein causes less loss of the edge information according to the profile comparison, and noticeably improves the local spatial resolution. In accordance with the edge information, the MAP-MRF-based SR approach can heighten the spatiotemporal resolution, and meanwhile preserve the texture information and produce smoother edges with sharper transitions and less motion blurring, compared with other algorithms. This is mainly because the WNS and multi-regularization in our method effectively exploit the spatiotemporal coherences. In summary, through the spatiotemporal SR, the visual quality is improved significantly, especially in terms of fidelity in the foreground. Figure 12: SR results of CACTI reconstruction results of traffic dataset with \(N_{f}=8\): (**a**) ground truth; (**b**) reconstructed frame 1 by GAP-acc + TV; (**c**) reconstructed frame 1 by GAP + b; (**d**) reconstructed frame 1 by proposed multi-regularization algorithm; (**e**) reconstructed frame 1 by spatial temporal algorithm super reconstruction based on 3D Steering Kernel Regression; (**f**) reconstructed frame by MAP-MRF-based spatial temporal super reconstruction approach; (**g**) the residual images of (**b**); (**h**) the residual images of (**c**); (**i**) the residual of image reconstructed by MAP-MRF-based approach with the initial LR sequence reconstructed GAP-acc + TV; (**j**) the residual of image reconstructed by MAP-MRF-based approach with the initial LR sequence reconstructed GAP + b; (**k**) the residual images of (**e**); (**l**) the residual images of (**f**). The calculation of regulation coefficient and weighted coefficient for the proposed approach depends on the estimation of motion vectors.