# Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission
## 4 Simulation Results
Regarding the demonstrations of performance of the proposed method, for the BCS coefficients in the red and green planes we set \(p_{e,1}=p_{e,2}=0.2\), and the BCS coefficients in the blue plane were treated as error-free transmissions or \(p_{e,1}=p_{e,2}=0.0\). In Figure 9a,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 9b,d, due to high correlation between color planes and protection with multiple description coding, the reconstructed image quality was significantly improved. Figure 8: Reconstruction of BCS coefficients for the three color planes: (**a**) EQ only; (**b**) EQ + AS; (**c**) QC only; and (**d**) QC + AS. In Figure 10, we provide three sets of angles \(\theta_{1}\) and \(\theta_{2}\) in MDC with \(r_{1}=r_{2}=1\) from 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 choose \(\theta_{1}=\frac{\pi}{3}\) 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 \(\theta_{1}=\frac{-\pi}{4}\). For Figure 10a,c,e, reconstruction was based on the equality constraint, while for Figure 10b,d,f, reconstruction was based on the quadratic constraint. Comparing the three selections, the orthogonal angles may lead to better performance to combat channel errors in reconstruction. Figure 9: 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. In Figure 11, we display the evaluations of reconstructed image qualities over the range of lossy probabilities between the range of 0 and 0.5, with a measurement rate of 0.1. We observed that with increased loss rates the inferior quality of the reconstructed images could be monitored. In addition, protection with multiple description coding, or the three curves at the upper portion, alleviated the effect caused by data loss, which led to better quality reconstructed images. Finally, we found that with the careful selection of the \(\varepsilon\) value from Equation (4), quadratic constraint performed slightly better than the equality constraint in reconstructed image quality. Figure 3:0 Demonstration of angle selection in multiple description coding with equality and quadratic constraints. BCS coefficients experienced a lossy rate of \(p_{e,1}=p_{e,2}=0.1\) in three planes. In Figures 12-16 we demonstrated the results of the third set of experiments for the color image Pasadena-houses with the size of \(1760\times 1168\). Unlike the test image cameraman in Figure 3a and ducks in Figure 7a, which are square-shared images, Figure 12a was a rectangular-shaped image. The color image was composed of three color planes, namely red, green, and blue. Figure 12a depicts the color image Pasadena-houses, and Figure 12b-d displays the entropy distributions of the three color planes for adaptive sampling (AS). Figure 13 presents the error-free transmission of BCS for Pasadena-houses. The measurement rate was set to \(\frac{12}{64}=0.1875\) for each color plane whether AS was applied or not. The reconstructed images were assessed with PSNR and SSIM. Figure 13a,b show the reconstruction for equality constraint (EQ) and quadratic constraint (QC), respectively, and the PSNR and SSIM values are also shown. Figure 13c,d present the reconstruction for EQ + AS and QC + AS, respectively. With adaptive sampling, better PSNR and SSIM performances were observed due to the local characteristics in entropy distribution. Again, QC performed slightly better than EQ. This observation fit for the color images Pasadena-houses in Figure 12, ducks in Figure 8, and the grey-level image cameraman in Figure 3:1  
Figure 3:2 Reconstructions for EQ and QC constraints for ducks with different lossy probabilities: (**a**) PSNR curves and (**b**) SSIM curves.