## 3 Experimental Scheme and Analysis of Results  
### Introduction to the Experimental Setup and Experimental Principles  
The SPI imaging scheme is shown in Figure 3, in which a target object illuminated by a light beam is imaged on a DMD, and then one of the light beams reflected from the DMD is captured by a barrel detector through a collection lens. As an indirect imaging method, the image can be retrieved by a correlation calculation between the modulation matrix and the actual captured single-pixel optical signal carrying information about the target object. Figure 2: Schematic diagram of the image reconstruction using a neural network. (**a**) Schematic diagram of network operation, (**b**) images reconstructed by the neural network with different sampling rates and different number of iterations. We assume that the pixelated target object image is \(T(x,y)\), which contains a total of \(N=x\cdot y\) pixel points. In SPI, a series of modulation patterns \(P_{i}(x,y)\) are usually loaded onto the DMD used to spatially modulate the beam carrying the object information, where \(i=1,2,...,N\) represents the number of modulation patterns. The DMD-modulated one-dimensional light intensity signal collected by the barrel detector can be denoted as \(y_{i}\), which corresponds to the result of the object image being modulated by a certain pair of scattering patterns, a process that can be mathematically represented as  
\[y_{i}=\int\limits_{x}\int\limits_{y}P_{i}(x,y)\cdot T(x,y)dxdy, \tag{13}\]  
The barrel signal for all submeasurements can be expressed as  
\[S=PT. \tag{14}\]  
We can use the known modulation pattern \(P\) and the detected barrel signal \(S\) to solve for the image of the target object. The signal can be expressed in terms of normalized intensity correlation as  
\[\mathrm{g}^{(2)}(x,y)=\frac{(1/N)\sum\limits_{i=1}^{N}S_{i}P_{i}(x,y)}{(1/N) \sum\limits_{i=1}^{N}S_{i}(1/N)\sum\limits_{i=1}^{N}P_{i}(x,y)}, \tag{15}\]  
Here, \(S\) is the ith(\(i=1,2,\cdots,N\)) single-pixel signal, \(P_{i}(x,y)\) is the ith modulation scatter, and x and y are the row pixel coordinates and column pixel coordinates of each modulation base of the DMD. It is well known that ToF cameras can simultaneously output intensity and depth data carrying information about the target object, both of which are derived from the number of photons received by the ToF sensor in a certain period of time. Their difference is that the intensity information can be obtained as directly as by using a detector, while the depth map is obtained by calculating the phase difference of different phase signals through a complex mathematical operation in Equation (8). However, they are essentially determined by the statistics of the number of photons. Therefore, when the ToF camera is used as a barrel detector, both intensity information and depth information can be used in the SPI system of Figure 3. That is, by replacing the barrel signal intensity information with depth information, Equation (15) still holds, and we have published this result in [69]. In order to verify the feasibility of the proposed scheme, based on the experimental setup in Figure 3, a ToF camera was used for the SPI experiments; we used a \(320\times 240\) pixel ToF camera (OPT8241, Texas Instruments, Dallas, TX, USA) instead of a barrel detector, and inserted a total reflective prism (TRP) between the DMD and the detector to regulate the optical path, and the rest of the experimental setup was similar to that of the conventional  
Figure 3: The schematic diagrams of SPI. SPI in Figure 3. In Figure 4, a flat object with an infrared light source at a wavelength of 850 nm is imaged with an imaging lens with a focal length of 50 mm on the surface of the optical unit of a DMD (DLP LightCrafter 4500, Texas Instruments), in which an all-reflecting prism is inserted in the optical path to accommodate the adjustment of the detection system.