# Single-Pixel Imaging Based on Enhanced Multi-Network Prior
## 1 Introduction
It is an enhanced deep learning method based on physical model, which builds a bridge between data-driven and model-driven algorithms to improve the reconstruction quality of single-pixel imaging [28; 29; 30; 31; 32; 33]. [PERSON] et al. [30] proposed an SPI method based on Fourier transform using untrained convolutional network. Although there is no need to train the dataset, it is necessary to use the output and label data of the neural network and the physical model to automatically optimize the network parameters. The imaging effect is better than other algorithms when the sampling rate is lower than 12.5%. [PERSON] et al. [31] proposed an untrained convolutional autoencoder network for SPI reconstruction. Although this method does not require pre-training on the dataset, it needs to automatically optimize the network parameters through the interaction between the neural network and the physical model. [PERSON] et al. [32] proposed a far-field super-resolution GI technique that incorporates the physical model for GI image formation into a deep neural network. The hybrid neural network incorporated into the physical model does not require pre-training on any dataset and can reconstruct far-field images with resolutions exceeding the diffraction limit. [PERSON] et al. [33] proposed an untrained attention U-Net for SPI, achieving superior reconstruction quality at sampling rates below 10%. The combination of physical models significantly improves the reconstruction quality, but this method is highly dependent on the accuracy of the physical model itself. The third method uses a traditional or enhanced measurement matrix to linearly measure the original image [34; 35; 36; 37; 38; 39; 40; 41; 42] and uses a neural network to reconstruct the target image within this linear framework. When the measurement rate is low, the results of traditional algorithms are usually affected by background noise or blurred lines, resulting in poor reconstruction results. Using neural networks improves the quality of reconstruction. [PERSON] et al. [39] proposed an enhanced encoding image similarity method for one-dimension signal in SPI. [PERSON] et al. [40] proposed an OIAE algorithm based on AE network to extract features for reconstruction. [PERSON] et al. [41] proposed a reconstruction method of SAE and multi-channel prior information based on SAE extracting prior information of different sample rates. However, SAE uses a simple double full connection, which limits the feature extraction ability. [PERSON] et al. [42] proposed a Unet++ SPI reconstruction method based on Unet++ and attention mechanism, achieving clear image reconstruction under the turbidity level of 80 NTU. Although single-pixel imaging based on SAE or Unet network has achieved good results, there is no multi-network single-pixel imaging method combining SAE and Unet. Therefore, we propose a multi-network single-pixel imaging method based on SAE and Unet. In order to make full use of the dimension information of the measurement value, the number of SAE coding network layers is designed to be four layers. In order to enhance its generalization, the group inverse is used to solve the decoding matrix of SAE. The Unet architecture employs a three-layer network structure, incorporating multi-scale convolutional kernels, sub-pixel convolution, and an attention mechanism to enhance its feature extraction ability. The reconstructed image is obtained by using the SAE network and Unet to extract feature fusion. In this way, the advantages of both networks are combined to obtain crucial image information and improve the image reconstruction quality. Moreover, our proposed network can be applied to SPI systems by training the sampling matrix in binary form. The effectiveness of the proposed network is verified by simulation and physical experiments. Our contributions are summarized as follows:  
* We propose an enhanced multi-network prior reconstruction method for SPI using SAE and Unet.