Butterworth filter-based ringing artifact suppression for low-sampling-rate single-pixel imaging

Single-pixel imaging (SPI) facilitates broad-spectrum imaging through a singular point detector; however, ringing artifacts resulting from the Gibbs phenomenon may arise at low sampling rates. To address this issue, we proposed a ringing suppression scheme that operates without the need for training. First, we conducted a quantitative analysis of the source of the ringing, empirically examining the relationship between Gibbs ringing and the transition steepness of the spectral window at the cutoff radius and showing a monotonic increase of ringing amplitude with the cutoff slope. Second, utilizing the Jinc-type point spread function associated with circular and Butterworth windows, we advocate for substituting the conventional 'hard cutoff' with a flat first-order Butterworth window and present criteria for selecting the order and cutoff coefficient. Third, the filter cutoff range is selected according to the sampling rate based on sensitivity analysis. The cutoff spectrum is multiplied point-by-point by the Butterworth window and subsequently inverse transformed. Experimental results demonstrated that the proposed Butterworth filtering technique achieves effective ringing suppression with high computational efficiency at low sampling rates (5% and 10%), which makes it well-suited for real-time SPI applications.