# Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission
## 4 Simulation Results
In Figure 5 we applied adaptive sampling and quadratic constraint with different selections of the value \(\varepsilon\) in Equation (4) for experiments. We chose \(\varepsilon=250\) for Figure 4(a),c,e, and \(\varepsilon=320\) for Figure 4(b),d,f. In Figure 4(a),b, we applied error-free transmission, or \(p_{e,1}=p_{e,2}=0.0\), over the two independent and lossy channels. We observed that Figure 4(a), or the one with \(\varepsilon=250\), performed slightly better. In Figure 4(c),d, we set \(p_{e,1}=0.1\) and \(p_{e,2}=0.0\), meaning that Channel 1 was lossy, and Channel 2 was error-free. Here we noticed that Figure 4(d), or the one with \(\varepsilon=320\), had better PSNR and SSIM values. We also noted that even though the PSNR value in Figure 4(d) was larger than that of Figure 4(c), the SSIM value was not. SSIM considers the local characteristics of the images, and PSNR takes the error of the whole image into account. Thus, there may sometimes be mismatches between the two measures. Finally, in Figure 4(e),f, we set \(p_{e,1}=p_{e,2}=0.1\). Due to data loss in both channels, reconstructions in Figure 4(e),f depict inferior results to their counterparts in Figure 4(c),d. Here, Figure 4(f), or the one with \(\varepsilon=320\), performed better than Figure 4(e). Based the performances depicted in Figure 5, we may conclude that with the careful selection of the tolerance value or, in this case, \(\varepsilon=320\), a better quality reconstructed image can be acquired. Figure 4: Reconstruction of BCS coefficients with equality constraint over lossy channels. In Figure 6 we present the evaluations of the reconstructed image quality over a range of lossy probabilities between 0 and 0.5, with a measurement rate of 0.1. We observed that the increase of loss tended toward inferior quality reconstructed images, as was expected. In addition, protection with multiple description coding 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, quadratic constraint performed slightly better than equality constraint in terms of reconstructed image quality. Figure 5: Reconstruction of BCS coefficients with quadratic constraint (QC) over lossy channels with protection. In Figures 7-11 we demonstrate the second set of experiments for the color image ducks with a size of \(1024\times 1024\). The color image is composed of three color planes, namely, red, green, and blue. Figure 7a depicts the color image ducks, and Figure 7b-d shows the entropies in the three color planes for adaptive sampling (AS). Figure 6: Reconstructions for EQ and QC constraints for cameraman with different lossy probabilities: (**a**) Peak Signal-to-Noise (PSNR) curves and (**b**) Structural Similarity (SSIM) curves. Figure 7: Entropy distributions for adaptive sampling in ducks: (**a**) Original image; (**b**) The entropy in the red plane; (**c**) The entropy in the green plane; (**d**) The entropy in the blue plane. Figure 8 presents the error-free transmission of BCS for ducks. The measurement rate was set to \(\frac{12}{64}=0.1875\) for each color plane, and reconstructed images can be assessed with the PSNR and SSIM measures. Note that the abbreviations in the captions of Figure 8 are identical to their counterparts in Figure 3. Figure 8a,b show only the reconstruction for equality constraint (EQ) and quadratic constraint (QC), respectively. The PSNR and SSIM values are also shown. Figure 8c,d present the reconstruction for EQ + AS and QC + AS, respectively. With adaptive sampling, better PSNR and SSIM performance can be observed. In addition, the performance with QC was slightly better than that with Equation (9). This observation for the color image of ducks in Figure 8 is similar to that for the grey-level image of cameraman in Figure 3.  
In Figure 9, we apply the multiple description coding of Equation (9) to protect the BCS coefficients with EQ or QC constraints.