A Novel Bound for Fourier Ring Correlation in Resolution Analysis

This work proposes a novel data-driven approach for computing the resolution number of a given image using the well-established Fourier Ring/Shell Correlation (frc/fsc) technique. The proposed method eliminates the need for the user to select a threshold criterion in a heuristic way, a requirement in current methodologies. To achieve this, the approach leverages linear algebra—specifically, Niculescu’s result—and concepts from information theory, demonstrating that the resolution number is directly linked to the Fisher information derived from each ring or shell in the Fourier domain. As a result, the methodology is entirely data-driven, requiring no prior information about the image under analysis. The mathematical framework’s consistency is validated through numerical experiments and tests with real data from x-ray coherent microscopy, tomography, cryo-EM and confocal microscopy, showing that the newly computed resolution numbers align with conventional metrics derived from the classical $1/2$-bit and $3\sigma$ thresholds. Furthermore, we highlight that the local resolution of images can vary significantly from the single resolution value typically provided by frc/fsc. This observation suggests that resolution maps may provide a more reliable framework for assessing resolution in microscopy.