Image denoising and deringing for fourier single-pixel imaging based on upgraded weighted nuclear norm minimization

Single-pixel imaging techniques have been extensively studied because of the low requirements for the detector resolution and the low equipment cost. However, a large amount of noise and ringing commonly occur in the reconstructed images via previous single-pixel imaging methods at ultra-low sampling rates, which limits the real applications. In this paper, a novel Fourier single-pixel imaging method is proposed to reconstruct high-quality single-pixel imaging images at ultra-low sampling rates, which involves the stages of Fourier single-pixel imaging, block matching, upgraded weight nuclear norm minimization, and aggregation. To decrease the computational burden while important image details, block matching and aggregation are employed for the blocks divided from the low-quality image reconstructed by Fourier single-pixel imaging. To adapt the proposed upgraded weight nuclear norm minimization to different contaminated images, an adaptive scheme for the iterative regularization parameter is proposed to update the traditional weight nuclear norm minimization. Experimental results indicate that the proposed Fourier single-pixel imaging method based on upgraded weight nuclear norm minimization exhibits the capacity to reliably and effectively reconstruct high-quality images for single-pixel imaging at low sampling rates, even at the sampling rate of 1 %. Experimental results also demonstrate that the proposed method performs better image reconstruction than some existing single-pixel imaging.