# Optimization Methods of Compressively Sensed Image Reconstruction Based on Single-Pixel Imaging
## 4 Experiments
### Experiments for DWT Optimization  
According to the good improvement results of above simulation experiments in reconstructing images _Building_ and _House_, parameter \(p\) was set to 0.996 and our method of optimizing DWT was further applied to our single-pixel imaging system for practical imaging experiments. 0-1 binary sensing matrix and part Hadamard binary sensing matrix are used as the masks to drive and encode the DMD sequences in our imaging system, as shown in Figure 1a. We used the single-pixel camera to take images of two scenes of the distant buildings at the sampling rate of 0.25, and reconstructed images of the two imaging scenes are shown in Figures 8a-d and 9a-d. The close-up regions marked with a red solid rectangle were enlarged, as shown in Figures 8a and 9a.  
According to the practical imaging results of Figures 8a-d and 9a-d, we can give the qualitative evaluation from the visual quality. Our wavelet optimization method effectively improves the imaging quality. For both of the 0-1 binary sensing matrix and the part Hadamard sensing matrix, the reconstructed images by our method have better visual quality with clearer image details, lower noise and better contrast, and the window contours are more obvious and sharper in Figure 8c,d and Figure 9c,d.  
Because there are not original images as the evaluation benchmarks for the two imaging scenes, in order to quantitatively analyze and evaluate the imaging quality, we define the signal to noise ratio (SNR) to quantitatively calculate the imaging accuracy, as expressed in Equation (33):  
\[SNR(dB)=|_{f}-I_{b}|/\left((_{f}+\sigma_{b})/2\right)=\frac{2\left|I_{f}-I_{b} \right|}{\sigma_{f}+\sigma_{b}}, \tag{33}\]  
where \(I_{f}\) is the average grayscale intensity of the feature (here calculated from the pixel grayscale highlighted by the solid green rectangle in Figures 8a and 9a), \(I_{b}\) is the average grayscale intensity of the background (calculated from the pixel grayscale highlighted by the solid blue rectangle in Figures 8a and 9a), \(\sigma_{f}\) and \(\sigma_{b}\) are the standard deviations of the grayscale intensities in the feature and the background respectively.  
Figure 8: The imaging results of scene 1 before and after using the proposed optimization methods at the sampling rate of 0.25 (”00” denotes the traditional imaging method before optimization; “01” denotes the imaging method after only optimizing wavelet decomposition basis; “10” denotes the imaging method after only optimizing binary sensing matrices; “11” denotes the imaging method after optimizing both wavelet decomposition basis and binary sensing matrices simultaneously).  
According to the evaluation index of Equation (33), we obtained the statistic SNRs table of Figures 8a-d and 9a-d, as shown in Table 1. In order to express each imaging method conveniently and concisely, we used the \"00\" \"01\" \"10\" \"11\" to denote the four different imaging methods. From Table 1, one can know that, whether for the 0-1 binary matrix or the part Hadamard matrix, the SNRs of reconstructed images for both two imaging scenes have been very evidently improved after our  
Figure 9: The imaging results of scene 2 before and after using the proposed optimization methods at the sampling rate of 0.25 (“00” denotes the traditional imaging method before optimization; “01” denotes the imaging method after only optimizing wavelet decomposition basis; “10” denotes the imaging method after only optimizing binary sensing matrices; “11” denotes the imaging method after optimizing both wavelet decomposition basis and binary sensing matrices simultaneously).  
method optimizing wavelet decomposition basis, as shown by the bold in Table 1. Therefore, the data results of Table 1 quantitatively demonstrate the superiority and effectiveness of our proposed DWT optimization method.