# Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission
## 4 Simulation Results
Figure 3:3 _Cont._  
In Figure 14 we applied multiple description coding from Equation (9) to protect the BCS coefficients with EQ or QC constraints. By following the scenarios in Figure 9 for the BCS coefficients in the red and green planes, we set \(p_{e,1}=p_{e,2}=0.2\). The BCS coefficients in the blue plane were treated as error-free transmissions, or \(p_{e,1}=p_{e,2}=0.0\). In Figure 14a,c, because the BCS coefficients could be lost during transmission, the degradation of the reconstructed image was affected whether or not the EQ or QC constraints were applied. In Figure 14b,d, due to the high correlation between color planes and the protection with multiple description coding, the reconstructed image quality was significantly improved. Figure 3:4 Entropy distributions for adaptive sampling in Pasadena-houses: (**a**) original image; (**b**) entropy in the red plane; (**c**) entropy in the green plane; and (**d**) entropy in the blue plane. Figure 3:5 Reconstruction of BCS coefficients for the three color planes: (**a**) EQ only; (**b**) EQ + AS; (**c**) QC only; and (**d**) QC + AS. In Figure 15, by following the same parameter settings used in Figure 10, we provided three sets of selections of angles \(\theta_{1}\) and \(\theta_{2}\) in MDC with \(r_{1}=r_{2}=1\) in Equation (9). First, we chose \(\theta_{1}=\frac{\pi}{6}\) and \(\theta_{2}=\frac{-\pi}{6}\), which led to opposite signs between angles. Second, we chose \(\theta_{1}=\frac{\pi}{3}\) and \(\theta_{2}=\frac{\pi}{6}\), meaning that the two angles were orthogonal. Third, by combining the first two selections, we chose \(\theta_{1}=\frac{\pi}{4}\) and \(\theta_{2}=\frac{-\pi}{4}\). For Figure 15a,c,e, reconstruction was based on the equality constraint, while for Figure 15b,d,f, reconstruction was based on the quadratic constraint. Comparing the three selections, angles that were orthogonal may have led to better performance combatting channel errors in reconstruction. In Figure 16 we demonstrated the evaluations of reconstructed image quality over a range of lossy probabilities between 0 and 0.5, with the measurement rate of 0.1. We observed that, with increased loss rates, inferior quality reconstructed images were seen whether or not the protection was deployed. In addition, protection with multiple description coding, or the three curves at the upper portion in Figure 16a,b, alleviated the effect of data loss, which led to better quality reconstructed images. Figure 3:6 Demonstration of lossy transmission in the red and green planes: (**a**) EQ + AS; (**b**) EQ + AS with MDC; (**c**) QC + AS; and (**d**) QC + AS with MDC. Figure 3:7 _Cont._  
From the results of the three sets of experiments, which corresponded to the three test images presented above, cameraman, ducks, and Pasadena-houses, protection of BCS with multiple description coding pointed to the applicability for transmitting over lossy channels. MDC worked together with EQ or QC reconstruction methods for BCS signals. Compensation between received descriptions with MDC helped reduce the effects of lossy channels. The alleviation of reconstructed image quality with error resilient coding is coveted. Figure 3:8 Reconstructions for EQ and QC constraints for Pasadena-houses with different lossy probabilities: (**a**) PSNR curves and (**b**) SSIM curves. Figure 3:9 Demonstration of angle selection in multiple description coding with equality and quadratic constraints. BCS coefficients experience lossy rate of \(p_{e,1}=p_{e,2}=0.1\) in three planes.