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

T.-a. Pham, E. Soubies, D. Sage, M. Unser

Best student paper award, Proceedings of the Sixteenth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'19), Venice, Italian Republic, April 8-11, 2019, pp. 321-324.

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.

AUTHOR="Pham, T.-a. and Soubies, E. and Sage, D. and Unser, M.",
TITLE="Closed-Form Expression of the {F}ourier Ring-Correlation for
        Single-Molecule Localization Microscopy",
BOOKTITLE="Proceedings of the Sixteenth IEEE International Symposium on
        Biomedical Imaging: From Nano to Macro ({ISBI'19})",
address="Venice, Italian Republic",
month="April 8-11,",
note="Best student paper award")

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