Fourier Ring Correlation and Anisotropic Kernel Density Estimation Improve Deep Learning Based SMLM Reconstruction of Microtubules - Berberich, Andreas; Kurz, Andreas; Reinhard, Sebastian; Paul, Torsten Johann; Burd, Paul Ray; Sauer, Markus; Kollmannsberger, Philip (Frontiers in Bioinformatics, 2021)
Single-molecule super-resolution microscopy (SMLM) techniques such as dSTORM can reveal biological structures down to the nanometer scale, but with further improvements, e.g., in combination with expansion microscopy, the density of fluorescent markers becomes a limiting factor for resolution. Artificial deep neural networks can learn to reconstruct dense super-resolved structures such as microtubules from a sparse, noisy set of data points. This approach requires a robust method to assess the quality of a predicted density image and to quantitatively compare it to a ground truth image. Such a quality measure needs to be differentiable to be applied as loss function in deep learning. We developed a new trainable quality measure based on Fourier Ring Correlation (FRC) and used it to train deep neural networks to map a small number of sampling points to an underlying density. Smooth ground truth images of microtubules were generated from localisation coordinates using an anisotropic Gaussian kernel density estimator. We show that the FRC criterion ideally complements the existing state-of-the-art multi-scale structural similarity index, since both are interpretable and there is no trade-off between them during optimisation. The TensorFlow implementation of our FRC metric can easily be integrated into existing deep learning workflows.