Image Reconstruction Based on Gaussian Smooth Compressed Sensing Fractional Order Total Variation Algorithm

In view of the gradient effect caused by the gradient effect of the Total Variation (TV) algorithm and the environmental noise in the single pixel imaging system, an image reconstruction based on the Gaussian Smooth compressed sensing Fractional Order Total Variation algorithm (FOTVGS) is proposed. Fractional differential loss of low-frequency components of the image increases the high-frequency components of the image to achieve the purpose of enhancing image details. The Gaussian smoothing filter operator updates the Lagrangian gradient operator to filter out the additive white Gaussian noise caused by the differential operator. Simulation results show that, compared with other four similar algorithms, the algorithm can achieve the maximum Peak Signal-to-Noise Ratio (PSNR) and Structural SlMilarity(SSIM) at the same sampling rate and noise level. When the sampling rate is 0.2, compared with the Fractional Order Total Variation (FOTV) algorithm, the maximum PSNR and SSIM increase by 1.39 dB (0.035) and 3.91 dB (0.098) respectively. It can be proved that this algorithm can improve the reconstruction quality of the image in the absence of noise and noise, especially in the case of noise, the quality of image reconstruction is greatly improved. The proposed algorithm provides a feasible solution for image reconstruction of noise caused by environment in single-pixel imaging and other computing imaging system.