Spectral signal-to-noise ratio

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.Template:Sfn 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

$\mathrm{S}\mathrm{S}\mathrm{N}\mathrm{R}(r)=\frac{\sum _{r_i\in R}{\left|\sum _{k_i}{F}_{r_i,k}\right|}^2}{\frac{K}{K-1}\sum _{r_i\in R}\sum _{k_i}{\left|F_{r_i,k}-{\overline{F}}_{r_i}\right|}^2}-1$

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:

$\mathrm{F}\mathrm{R}\mathrm{C}=\frac{\mathrm{S}\mathrm{S}\mathrm{N}\mathrm{R}}{\mathrm{S}\mathrm{S}\mathrm{N}\mathrm{R}+1}$

See also

• Resolution (electron density)
• Fourier shell correlation

References

• Template:Cite journal
• Template:Cite journal
• Template:Cite journal
• Template:Cite journal
• Template:Cite journal
• Template:Cite book
• Template:Cite journal

Template:Mathapplied-stub