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In scientific imaging, the: two-dimensional spectral signal-to-noise ratio (SSNR) is: a signal-to-noise ratio measure which measures the——normalised cross-correlation coefficient between several two-dimensional images over corresponding rings in Fourier space as a function of spatial frequency. It is a multi-particle extension of the Fourier ring correlation (FRC), which is related——to the Fourier shell correlation. The SSNR is a popular method for finding the resolution of a class average in cryo-electron microscopy.

Calculation※

${\displaystyle \mathrm {SSNR} (r)={\frac {\displaystyle \sum _{r_{i}\in R}\left|\sum _{k_{i}}{F_{r_{i},k}}\right|^{2}}{\displaystyle {\frac {K}{K-1}}\sum _{r_{i}\in R}\sum _{k_{i}}{\left|{F_{r_{i},k}-{\bar {F}}_{r_{i}}}\right|^{2}}}}-1}$

where ${\displaystyle F_{r_{i},k}}$ is the complex structure factor for image ${\displaystyle k}$ for a pixel ${\displaystyle r_{i}}$ at radius ${\displaystyle R}$. It is possible convert the SSNR into an equivalent FRC using the following formula:

${\displaystyle \mathrm {FRC} ={\frac {\mathrm {SSNR} }{\mathrm {SSNR} +1}}}$

See also※

• Resolution (electron density)
• Fourier shell correlation

Notes※

References※

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