# Image quality measurements and denoising using Fourier Ring Correlations

arXiv: https://arxiv.org/abs/2201.03992 · HTML: https://mlsanity.com/paper/2201.03992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 11 Jan 2022.

## Builds on (most cited first, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [Probabilistic Noise2Void: Unsupervised Content-Aware Denoising](https://mlsanity.com/paper/1906.00651/) (2019)
- [Loss Functions for Neural Networks for Image Processing](https://mlsanity.com/paper/1511.08861/) (2015)
- [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019)
- [Fully Unsupervised Probabilistic Noise2Void](https://mlsanity.com/paper/1911.12291/) (2019)

## Built on by (most cited first, 1 of 1)

- [Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcasting](https://mlsanity.com/paper/2410.23159/) (2024)

## Abstract (arXiv)

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.