# Single-Pixel Imaging Based on Enhanced Multi-Network Prior
## 1 Introduction  
Single-pixel imaging (SPI) is also known as computational ghost imaging. Different from the conventional imaging methods that rely on detector pixel arrays, it employs point detectors lacking spatial resolution to capture intensity data. Subsequently, the measured light intensity values are combined with a corresponding measurement matrix to reconstruct the image. Owing to its high sensitivity, wide spectrum, and low cost, SPI has found successful applications in numerous fields, particularly in scenarios where conventional imaging techniques are either prohibitively expensive or technologically unfeasible [1, 2, 3, 4]. Typically, it could be utilized in infrared imaging [5], 3D imaging [6], X-ray imaging [7], remote sensing [8], hyperspectral imaging [9], terahertz imaging [10] and super-resolution imaging [11]. Reconstructing high-quality images with few measurements and short reconstruction time has always been the primary goal of SPI. Limited by hardware facilities, the fastest refresh rate of DMD currently used is only 22 kHz. There are two primary strategies to achieve faster single-pixel imaging. The first approach is to boost the modulation speed by designing LED arrays and rotating masks, which operates independently of the speed of DMD [12, 13, 14]. The second approach entails employing advanced algorithms to decreasethe number of required measurements [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. In this work, we mainly focus on the advanced algorithms. With the rapid advancement of deep learning and neural networks, an increasing number of methods have adopted neural networks to facilitate fast imaging and high-quality image reconstruction. Currently, the mainstream methods in this field can be divided into three categories, which will be described in detail below. The first approach involves end-to-end joint learning of both sampling and reconstruction processes using neural networks [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. In this framework, the trained neural network weights serve as the measurement matrix, typically demonstrating superior performance in terms of both reconstruction speed and quality. [PERSON] et al. [19] proposed an FSPI under-sampling optimization method based on generative adversarial networks and attention mechanisms. [PERSON] et al. [20] proposed a variable generative network enhanced SPI algorithm VGNet. [PERSON] et al. [21] proposed a generative adversarial network single-pixel imaging algorithm MAID-GAN and MAID-GAIN+ that uses measurement values as auxiliary inputs. [PERSON] et al. [22] proposed an enhanced SPI reconstruction algorithm using transformer network with adaptive feature refinement. [PERSON] et al. [23] proposed an adaptive coarse-to-fine sampling method, which samples step by step according to the image and quality indicators, and finally uses GAN for depth image reconstruction. [PERSON] et al. [24] proposed a new Fourier SPI imaging high-quality reconstruction method based on diffusion model. [PERSON] et al. [25] proposed a diffusion model single pixel imaging algorithm DGRN with gradient descent guidance. [PERSON] et al. [26] proposed a DSPIM method based on conditional diffusion model and autoencoder network joint training and reconstruction for SPI. [PERSON] et al. [27] proposed a single-pixel computational imaging method based on a multi-input mutual supervision network. The above is the research results of the end-to-end generated model. Nevertheless, the number of network parameters grows exponentially with the size of the reconstructed image, posing scalability challenges. Neural networks have proven particularly effective in optimizing the simulation process of single-pixel reconstruction. Experimental results indicate a significant reduction in system complexity at low measurement rates (MR). The second approach is an untrained reconstruction network that does not need to be trained on the dataset.