Spectral signal-to-noise ratio

In applied mathematics, the two-dimensional Spectral signal-to-noise ratio (SSNR) measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings in Fourier space as a function of spatial frequency (Unser 1987). 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

$SSNR (r) = \frac{\displaystyle\sum_{r_i \in R}\left|\sum_{k_i}{ F_{r_i,k} }\right|^2} {\displaystyle \frac{K}{K-1} \sum_{r_i \in R}\sum_{k_i}{ \left|{ F_{r_i,k} - \bar{F}_{r_i}}\right|^2}} -1$

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

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

See also

• Resolution (electron density)
• Fourier shell correlation

Notes

References

• Unser, M.; Trus, B.L.; Steven, A.C. (1987). "A New Resolution Criterion Based on Spectral Signal-To-Noise Ratios". Ultramicroscopy 23 (1): 39–51. doi:10.1016/0304-3991(87)90225-7. PMID 3660491.
• Harauz, G.; M. van Heel (1986). "Exact filters for general geometry three dimensional reconstruction". Optik 73: 146–156.
• van Heel, M. (1982). "Detection of objects in quantum-noise limited images". Ultramicroscopy 8: 331–342. doi:10.1016/0304-3991(82)90258-3.
• Saxton, W.O.; W. Baumeister (1982). "The correlation averaging of a regularly arranged bacterial cell envelope protein". J Microscopy 127: 127–138. doi:10.1111/j.1365-2818.1982.tb00405.x.
• Böttcher, B.; Wynne, S.A.; Crowther, R.A. (1997). "Determination of the fold of the core protein of hepatitis B virus by electron microscopy". Nature 386 (6620): 88–91. doi:10.1038/386088a0. PMID 9052786.
• Frank, Joachim (2006). Three-Dimnsional Electron Microscopy of Macromolecular Assemblies. New York: Oxford University Press. ISBN 0-19-518218-9.
• van Heel, M.; Schatz, M. (2005). "Fourier shell correlation threshold criteria". Journal of Structural Biology 151 (3): 250–262. doi:10.1016/j.jsb.2005.05.009. PMID 16125414.