  Image quality is a nebulous concept with different meanings to different
people. To quantify image quality a relative difference is typically calculated
between a corrupted image and a ground truth image. But what metric should we
use for measuring this difference? Ideally, the metric should perform well for
both natural and scientific images. The structural similarity index (SSIM) is a
good measure for how humans perceive image similarities, but is not sensitive
to differences that are scientifically meaningful in microscopy. In electron
and super-resolution microscopy, the Fourier Ring Correlation (FRC) is often
used, but is little known outside of these fields. Here we show that the FRC
can equally well be applied to natural images, e.g. the Google Open Images
dataset. We then define a loss function based on the FRC, show that it is
analytically differentiable, and use it to train a U-net for denoising of
images. This FRC-based loss function allows the network to train faster and
achieve similar or better results than when using L1- or L2- based losses. We
also investigate the properties and limitations of neural network denoising
with the FRC analysis.
