Fourier ring correlation simplifies image restoration in fluorescence microscopy

Fourier ring correlation (FRC) has recently gained some popularity among (super-resolution) fluorescence microscopists as a straightforward and objective method to measure the effective resolution of a microscopy image. While the knowledge of the numeric resolution value is helpful in e.g. interpreting imaging results, much more practical use can be made of FRC analysis -- in this article we propose novel blind image restoration methods enabled by it. We apply FRC to perform image de-noising by frequency domain filtering. We propose novel blind linear and non-linear image deconvolution methods that use FRC to estimate the effective point-spread-function, directly from the images, with no need for prior knowledge of the instrument or sample characteristics. The deconvolution is shown to work exquisitely with both two- and three-dimensional images. We also show how FRC can be used as a powerful metric to observe the progress of iterative deconvolution. While developing the image restoration methods, we also addressed two important limitations in FRC that are of more general interest: how to make FRC work with single images and with three-dimensional images with anisotropic resolution.