Closed-Form Expression of the Fourier Ring-Correlation for Single-Molecule Localization Microscopy

Thanh-An Pham (1) , Emmanuel Soubies (1) , Daniel Sage (1) , Michael Unser (1)

1 Biomedical Imaging Group [Lausanne]

Single-molecule localization microscopy (SMLM) is a popular microscopic technique that achieves super resolution imaging by localizing individual blinking molecules in thousands of frames. Therefore , the reconstructed high-resolution image is a combination of millions of point sources. This particular computational reconstruction leads to the question of the estimation of the image resolution. Fourier-ring correlation (FRC) is the standard tool for assessing the resolution. It has been proposed for SMLM by computing a discrete correlation in the Fourier domain. In this work, we derive a closed-form expression to compute the continuous FRC. Our implementation provides an exact FRC and an alternative to compute a parameter-free FRC. In addition, it gives insights on the discrepancy of the discrete FRC and yields a rule to select its parameters such as the spatial sampling step or the width of the kernel used as density estimator.

Mots clés: Single-molecule localization microscopy; Fourier-ring correlation; image resolution

Domaines: Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]; Optique / photonique; Traitement du signal et de l'image [eess.SP]

Thanh-An Pham, Emmanuel Soubies, Daniel Sage, Michael Unser. Closed-Form Expression of the Fourier Ring-Correlation for Single-Molecule Localization Microscopy. ISBI 2019 - IEEE International Symposium on Biomedical Imaging, Apr 2019, Venise, Italy. ⟨hal-02048083⟩