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Single-pixel imaging is an advanced computational imaging technique based on compressive sensing that offers higher signal-to-noise ratio and broader application scope compared to traditional imaging techniques. However, conventional reconstruction algorithms suffer from issues such as long processing time and low reconstruction accuracy during the sampling and reconstruction processes. Deep learning-based compressed reconstruction networks can circumvent the complex iterative computations of traditional algorithms and achieve fast, high-quality reconstruction. In this paper, we propose a Variational Multi-Scale Error Compensation Network (VMSE) based on variational autoencoders. VMSE designs an error compensation network to enhance the feature representation capability of the sampling reconstruction network. We employ multiple latent variables to generate error features at different scales in the intermediate layers of the error compensation network, compensating the reconstructed image. Additionally, we design a module that simultaneously learns in the spatial and frequency domains, which is used for upsampling and complementing the missing high-frequency information in the frequency domain. On the MNIST dataset, when the sampling rate is 0.025, VMSE achieved higher Peak Signal-to-Noise Ratio(PSNR) and Structural Similarity Index(SSIM) scores, especially with an SSIM score of 0.963, significantly surpassing Reconnet and DR2Net's scores of 0.930 and 0.920, respectively. This was further corroborated by practical experiments, where at low sampling rates, VMSE could reconstruct outlines more clearly compared to TVAL3.

Reconstructing high-quality images at low measurement rate is one of the research objectives for single-pixel imaging (SPI). Deep learning based compressed reconstruction methods have been shown to avoid the huge iterative computation of traditional methods, while achieving better reconstruction results. Benefiting from improved modeling capabilities under the constant game of generation and identification, Generative Adversarial Networks (GANs) has achieved great success in image generation and reconstruction. In this paper, we proposed a GAN-based compression reconstruction network, MPIGAN. In order to obtain multiple prior information from the dataset and thus improving the accuracy of the model, multiple Autoencoders are trained as regularization terms to be added to the loss function of the generative network, and then adversarial training is performed with a multi-label classification network. Experimental results show that our scheme can significantly improve reconstruction quality at a very low measurement rate, and reconstruction results are better than the existing network.