# Optimization Methods of Compressively Sensed Image Reconstruction Based on Single-Pixel Imaging
## 4 Experiments
### Experiments for Binary Sensing Matrix Optimization  
In order to test the performance of our proposed algorithm of optimizing traditional binary sensing matrix and get the empirical values of parameters in Section 3.4, we also conducted simulation experiments of reconstructing images _Building_ and _House_ by using our optimized binary measurement matrices. After testing some values, we found empirically that these parameters perform relatively well that \(\xi=0.01\), \(\alpha_{\text{min}}=1\times 10^{-3}\), \(\alpha_{\text{max}}=1\times 10^{3}\), and \(\tau=0.35\) in the loss Equation (15). DWT matrix was used as the known decomposition basis in our experiments. Table 2 is the experiments' statistic results of reconstructing images _Building_ and _House_ before and after optimizing the binary sensing matrices with \(m=64\) and \(n=256\). From Table 2, one can know that, after optimizing the traditional 0-1 binary sensing matrix and part Hadamard binary sensing matrix by using our proposed algorithm, the optimized binary measurement matrices enhance the PSNRs of reconstructed images very significantly by about 2 to 3 dB and enhance the SSIMs by about 0.1, and the reconstructed images have higher precision. Then, the new optimized binary measurement matrices were fixed as the deterministic binary sensing matrices that were further applied to our single-pixel camera for practical imaging experiments. The experimental results are shown in Figures 8e,f and 9e,f and the corresponding SNRs are given in Table 3.  
As shown in Figures 8e,f and 9e,f, compared with Figures 8a,b and 9a,b of traditional methods, after using the new optimized binary measurement matrices in our imag \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sensing Matrix**} & \multicolumn{2}{c}{**Imaging Scene 1**} & \multicolumn{2}{c}{**Imaging Scene 2**} \\ \cline{2-5}  & **00** & **01** & **00** & **01** \\ \hline
0–1 binary & 11.2559 & **20.2571** & 27.8079 & **39.8900** \\ Hadamard & 13.2825 & **19.4724** & 29.7208 & **38.6189** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: SNRs (dB) of the imaging results of our single-pixel camera before and after optimizing wavelet decomposition basis (“00” denotes the traditional imaging method before optimization; “01” denotes the new imaging method after optimizing wavelet decomposition basis). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sensing Matrix**} & \multicolumn{2}{c}{**Building**} & \multicolumn{2}{c}{**House**} \\ \cline{2-5}  & **00** & **10** & **00** & **10** \\ \hline
0–1 binary & 21.3081/0.35986 & **24.0976/0.47856** & 19.3882/0.31822 & **22.3992/0.42724** \\ Hadamard & 21.4714/0.38021 & **23.7491/0.46868** & 19.7671/0.34684 & **21.8880/0.42742** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PSNRs (dB)/SSIMs of reconstructed images _Building_ and _House_ before and after optimizing binary sensing matrices (“00” denotes the traditional method before optimization; “10” denotes the new method after optimizing binary sensing matrices). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sensing Matrix**} & \multicolumn{2}{c}{**Imaging Scene 1**} & \multicolumn{2}{c}{**Imaging Scene 2**} \\ \cline{2-5}  & **00** & **01** & **00** & **01** \\ \hline
0–1 binary & 11.2559 & **23.1755** & 27.8079 & **45.1885** \\ Hadamard & 13.2825 & **21.0404** & 29.7208 & **42.4284** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SNRs (dB) of the imaging results of our single-pixel camera before and after optimizing binary sensing matrices (“00” denotes the traditional imaging method before optimization; “10” denotes the new imaging method after optimizing binary measurement matrices). quality of two scenes has been evidently improved with less visual artifacts and higher contrast, the reconstructed images have less distortion and noise is evidently suppressed. In Figures 8e,f and 9e,f, the contours become more clear and the edges get sharper, and the details of the locally enlarged regions are also richer.