Generalization of the two-point-source resolution criterion in the presence of noise

The two-point-source resolution criterion is widely used to quantify the performance of imaging systems. The two main approaches for the computation of the two-point-source resolution are the detection theoretic and visual analyses. The first assumes a shift-invariant system and lacks the ability to incorporate two different point spread functions (PSFs), which may be required in certain situations like computing axial resolution. The latter approach, which includes the Rayleigh criterion, relies on the peak-to-valley ratio and does not properly account for the presence of noise. We present a heuristic generalization of the visual two-point-source resolution criterion using Gaussian processes (GP). This heuristic criterion is applicable to both shift-invariant and shift-variant imaging modalities. This criterion can also incorporate different definitions of resolution expressed in terms of varying peak-to-valley ratios. Our approach implicitly incorporates information about noise statistics such as the variance or signal-to-noise ratio by making assumptions about the spatial correlation of PSFs in the form of kernel functions. Also, it does not rely on an analytic form of the PSF.