Spectral signal-to-noise ratio

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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.


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[edit]



  • 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. 
  • 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.