Reading between the lines: interpolation as it impacts ringing suppression

Hard apertures in imaging systems create artifacts at discontinuous points in an image. When we zoom in on such an image, Gibbs ringing can be a factor in the confusion of small features with artifacts, or in errors in measurements made of the features. In previous works, we have systemically analysed certain algorithms for suppressing artifacts, and developed metrics and procedures to make a quantifiable comparison between algorithms in that field. A common assumption in the literature is that zero-padding in the Fourier domain (sinc interpolation) is used for the zoom algorithm. Other algorithms make use of linear interpolation for a similar reason. In this paper, we analyse several interpolation formulae and compare them with sinc interpolation in a quantitative fashion. We further consider the interaction of the interpolation formulae with filtered Fourier reconstruction. Our results are foundational to establishing a quantitative evidence base for preferring certain ringing suppression algorithms over others, and provide grounds for revisiting assumptions that have long stood in commercial imaging pipelines.