Neha Patil (Editor)

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.

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

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:

F R C = S S N R S S N R + 1

References

Spectral signal-to-noise ratio Wikipedia
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