Self Fourier shell correlation: properties and application to cryo-ET

Abstract

The Fourier shell correlation (FSC) is a measure of the similarity between two signals computed over corresponding shells in the frequency domain and has broad applications in microscopy. In structural biology, the FSC is ubiquitous in methods for validation, resolution determination, and signal enhancement. Computing the FSC usually requires two independent measurements of the same underlying signal, which can be limiting for some applications. Here, we analyze and extend on an approach proposed by Koho et al. [1] to estimate the FSC from a single measurement. In particular, we derive the necessary conditions required to estimate the FSC from downsampled versions of a single noisy measurement. These conditions reveal additional corrections which we implement to increase the applicability of the method. We then illustrate two applications of our approach, first as an estimate of the global resolution from a single 3-D structure and second as a data-driven method for denoising tomographic reconstructions in electron cryo-tomography. These results provide general guidelines for computing the FSC from a single measurement and suggest new applications of the FSC in microscopy.

Denoising, Deblurring, and optical Deconvolution for cryo-ET and light microscopy with a physics-informed deep neural network DeBCR

“…FRC evaluation indicated that DeBCR restored a significantly larger amount of information across all frequencies compared to the other methods. Furthermore, by analyzing even/odd volumes, we estimated the noise spectrum 52 from the difference between two groups of volumes (see Supplementary materials, Fig. S4).…”