## 3 Experimental Scheme and Analysis of Results
### Experimental Results and Cause Analysis  
Our experiments are conducted under indoor conditions with ambient light to recover the target object to be measured, using the scheme shown in Figure 4 for the acquired ToF intensity information. The reconstructed target shown in Figure 5a is an object with a pixel value of \(32\times 32\) size. In order to highlight the superiority of our proposed method, Figure 5b shows the ToF intensity map obtained directly with the utilized ToF camera, which has a noticeable background noise and lower contrast compared to the original image in Figure 5a. In our experiments, whichever algorithm is used, the bucket signal is obtained by summing the intensities of all pixels in the region of interest of the ToF sensor and synchronizing them with the Hadamard base projected onto the DMD. Four commonly used image reconstruction algorithms are selected including CGI algorithm, Base Tracking (BP) algorithm, Total Variation Augmented Lagrangian Alternating Direction (TVAL3) algorithm and DL algorithm for recovering the images in the following experiments. As shown in Figure 5, the images are reconstructed at sampling rates of 6.25%, 12.5%, 18.75%, 25%, 31.25% and 37.5%. Figure 4: The schematic diagrams of SPI based on a ToF camera. Figure 5: Experimental results of imaging reconstruction using intensity images at different SRs. (**a**) Target object, (**b**) ToF image, (**c**–**f**) the recovered images by CGI, BP, TVAL3, and DL. The SRs from left to right is 6.25%, 12.5%, 18.75%, 25%, 31.25% and 37.5%. In Figure 5, When the sampling rate is 6.25%, BP reconstructs the image of the object, which can hardly be seen, only some streaks can be seen, while CGI, and TVAL3 algorithms can see the outline of the object image vaguely, and the untrained DL reconstruction based method can see the outline information of the object, and the reconstruction effect is better than the other three algorithms. When the sampling rate is 12.5%, the CGI and TVAL3 algorithms can see the more blurred contour information, and the background noise is reduced, and the BP algorithm appears to have blurred contours, but the background noise is still large, which affects the object information. The untrained DL reconstruction-based method was able to reconstruct a clearer image of the object with less background noise. When the sampling rate is 18.75, the CGI, BP, and TVAL3 can all see a clearer image of the object to be measured, but it is clear that the image quality obtained using CGI and TVAL3 is higher than that of BP, and the effect of untrained DL is higher than that of the other three algorithms. When the sampling rate is 25%, the background noise of the images obtained by CGI, BP, and TVAL3 algorithms still exist, but it is obvious that the reconstruction of the object becomes clearer, and it can be seen that the reconstruction effect of CGI and TVAL3 is still better than that of BP, and the reconstruction results from the DL are clearer than the object's image. When the sampling rate is 37.5%, the CGI, BP, and TVAL3 are also able to obtain the reconstructed object image clearly, and the background noise information is greatly reduced, and the reconstructed image results become better with the increase in the sampling rate. In order to quantitatively assess the effectiveness of different methods for reconstructing images, we calculated the peak signal-to-noise ratio (PSNR) of each reconstructed image with respect to the original image, which is a commonly used metric for evaluating the quality of retrieved images, and is given by the following equation:  
\[PSNR=10\times\log_{10}(\frac{(2^{n}-1)^{2}}{MSE}), \tag{16}\]  
\[MSE=\frac{1}{mn}\sum_{i=1}^{m-1}\sum_{j=0}^{n-1}{(\hat{T}(i,j)-T(i,j))}^{2}, \tag{17}\]  
Here, \(\hat{T}\) is the reconstructed image and \(T\) is the original image. According to Equation (16), Figure 6 shows the quantitative analysis of the PSNR of the reconstructed images using the four methods at different sampling rates.