The single-pixel imaging system is a computational optical imaging technology that obtains the two-dimensional distribution information of the target through a single-pixel detector without spatial resolution. Compared with traditional direct imaging technology, it has a series of advantages such as high energy collection efficiency and high sensitivity. In the field of high-energy physical diagnosis technology it has broad application prospects. Aiming at the problem that the actual single-pixel compressed sensing imaging system has large reconstruction noise in complex diagnostic environments, this paper proposes and implements a single-pixel imaging system based on the block smooth projection Landweber quadratic reconstruction algorithm. According to the distribution characteristics of the algorithm's observation matrix and the digital micromirror hardware input requirements, the transformation of the actual projection observation matrix is realized, and the simulation analysis and experimental test of the single-pixel diagnosis are realized by using the quadratic reconstruction algorithm. The simulation results show that under the condition of a 20% to 30% sampling rate, the peak signal-to-noise ratio of the reconstructed image is greater than 20 dB, and the structural similarity is higher than 0.8. The single-pixel imaging platform is further built to complete the experimental research and verification. The experimental results show that the recovery effect of the target scene using the quadratic reconstruction algorithm model is better than the other two traditional algorithms. The quadratic reconstruction single-pixel imaging system can reconstruct a clear original image with a sampling rate of only 20%, and has good noise suppression characteristics.