# Fast Terahertz Coded-Aperture Imaging Based on Convolutional Neural Network
## 3 Results  
In this section, the feasibility of the DL based approach is verified by numerical experiments. Parameters in the imaging experiment are given in Table 1. The frequency range of the THz signal is from 330 GHz to 350 GHz. The 1-bit transmission-type coded aperture has \(60\times 60\) elements that are employed to modulate the phase of the transmitted signal by \(0^{0}\) or \(180^{0}\). The imaging area is divided into \(M=60\times 60\), and it is easy to calculate that the pixel interval is no larger than 0.005 m. The size of the target (\(T\)) is expressed as the number of non-zero scattering coefficients in imaging area [37], the ratio between \(T\) and \(M\) is considered the complexity of the target. Also, it is easy to know from the table that the spatial dimension of \(\mathbf{S}\) is 3600 \(\times\) 3600, which creates high imaging complexity. In practice, the scale of \(\mathbf{S}\) may be larger and this calculation is more complicated. Therefore, it is necessary to use a neural network to model \(\mathbf{S}\) implicitly. The network is implemented in Python version 3.6 using DL frameworkForlow version 1.8 and trained on a desktop computer with GPU NVIDIA 2080 and the CUDA edition is 9.0. The training took approximately 10 h, which is time-consuming but this procedure can be done in advance. Once trained, the target of interest can be restored instantly by inputting echo signal into the imaging network. The Adam optimization algorithm is employed to optimize weights, and the initial learning is \(10^{-3}\) which decays with the factor of 0.98 after each epoch. The batch size is 8 and the training lasts for 500 epochs. Two typical reconstruction algorithms for TCAI, the Sparse Bayesian Learning (SBL) algorithm and TVAL3 algorithm, were chosen to compete with the presented approach. To analyze the imaging performance of various algorithms, the Mean Square Error (MSE) is used as the quantitative index. In this paper, these test targets are composed of scattering points, and the corresponding scattering coefficients are a random value between zero and unity. All reconstruction results and MSE calculations were done on the computer with Inter Xeon Silver 4116 CPU except as specifically stated, and each MSE represents the average results 100 Monte Carlo trials and the shape of the target changes randomly in each trial. To investigate the validity of the imaging network, we first carried out simulation experiments at various targets and the results with SNR = 20 dB are shown Figure 3, and the ratio between the target size and the number of grid cells is \(T/M=11/3600\), \(T/M=\)17/120, \(T/M=\)431/3600, \(T/M=\)731/3600, \(T/M=\)71/200, \(T/M=\)37/60, respectively. It can be seen that the target can be successfully reconstructed whether it is made up of unit ideal point scatters or multi-value point scatters. For further investigating the imaging performance of the proposed method, the SBL algorithm [38] and TVAL3 algorithm [39] were implemented as comparisons. Figure 4 shows the reconstruction results of the \"smile\" whose scattering coefficients of all the point scatters are a random value between zero and unity. One can clearly see that the object can be recovered from the echo signal through the deep network-based algorithm as low as SNR = \(-5\) dB, despite the reconstruction results apparently being distorted and having many spurious scatterers just like other methods. However, the imaging quality gradually enhanced with the increase of SNR. Compared with SBL algorithm under all SNR levels, the proposed algorithm provides higher resolution results in which the scattering