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
S S N R ( r ) = ∑ r i ∈ R | ∑ k i F r i , k | 2 K K − 1 ∑ r i ∈ R ∑ k i | F r i , k − F ¯ r i | 2 − 1 {\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 F r i , k {\displaystyle F_{r_{i},k}} is the complex structure factor for image k {\displaystyle k} for a pixel r i {\displaystyle r_{i}} at radius R {\displaystyle R} . It is possible convert the SSNR into an equivalent FRC using the following formula:
F R C = S S N R S S N R + 1 {\displaystyle \mathrm {FRC} ={\frac {\mathrm {SSNR} }{\mathrm {SSNR} +1}}}
See also Resolution (electron density) Fourier shell correlation
Notes
References