# Optimization Methods of Compressively Sensed Image Reconstruction Based on Single-Pixel Imaging
## 4 Experiments
### Compressive Experiments  
In order to test the comprehensive performance of our methods in optimizing wavelet decomposition basis and binary sensing matrices, both the two optimization methods of wavelet decomposition basis and binary measurement matrices were simultaneously applied to our single-pixel camera at the sampling rate of 0.25, the imaging results are shown in Figures 8g,h and 9g,h and the corresponding SNRs are given in Table 4.  
It can be seen from Figures 8g,h and 9g,h that, after simultaneously optimizing the wavelet decomposition basis and binary sensing matrices by our proposed methods, the imaging visual quality of Figures 8g,h and 9g,h is significantly higher than that of Figures 8a,b and 9a,b, and the proposed methods can produce clearer and sharper results and recover the smaller details of the imaging scenes, and the reconstructed images are also closer to the real imaging scenes. Furthermore, compared with Figures 8a,b and 9a,b, our methods have favorably suppressed the column visual artifacts that were produced by the imaging method of column-by-column scanning and our methods play the important roles in reducing the noise of reconstructed images. From Table 4, one can know that the comprehensive performance of our two optimization methods is superior than either one optimization method alone. In addition, the two imaging scenes were reconstructed at six different sampling rates and the statistic SNRs results of the two reconstructed imaging scenes were calculated, and the curves of experimental results are shown in Figure 10.  
One can see that from Figure 10, for different compression sampling rates (SCR), our proposed optimization methods can effectively improve the accuracy and quality of images reconstruction. Compared to the traditional imaging method (\"00\") before optimization, whether the wavelet decomposition basis and the binary sensing matrices are optimized separately or simultaneously, the imaging SNRs and the accuracy of reconstructed images have been enhanced pretty obviously. Furthermore, our proposed methods of optimizing both the wavelet decomposition basis and the binary sensing matrices simultaneously (\"11\") achieve the best performance compared with the traditional method or either one optimization method alone. These experimental results have fully demonstrated the effectiveness of our proposed methods in optimizing the traditional wavelet decomposition basis and the conventional binary sensing matrices.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Sensing** \\ **Matrix** \\ \end{tabular} } & \multicolumn{4}{c}{**Imaging Scene 1**} & \multicolumn{4}{c}{**Imaging Scene 2**} \\ \cline{2-9}  & **00** & **01** & **10** & **11** & **00** & **01** & **10** & **11** \\ \hline
0–1 binary & 11.2559 & 20.2571 & 23.1755 & **25.2712** & 27.8079 & 39.8900 & 45.1885 & **50.4516** \\ Hadamard & 13.2825 & 19.4724 & 21.0404 & **22.6124** & 29.7208 & 38.6189 & 42.4284 & **45.6888** \\ \hline \hline \end{tabular}
\end{table}
Table 4: SNRs (dB) of the imaging results by optimizing binary sensing matrices and wavelet decomposition basis (“00” denotes the traditional imaging method before optimization; “01” denotes the imaging method after only optimizing wavelet decomposition basis alone; “10” denotes the imaging method after only optimizing binary sensing matrices; “11” denotes the imaging method after optimizing both wavelet decomposition basis and sensing measurement matrices simultaneously).