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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 {{harv|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]].
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| == Calculation == | |
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| :<math> | |
| SSNR (r)
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| =
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| \frac{\displaystyle\sum_{r_i \in R}\left|\sum_{k_i}{ F_{r_i,k} }\right|^2}
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| {\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
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| </math>
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| <!--
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| :<math>
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| =
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| \frac{\displaystyle\sum_{r_i \in R}\left|\sum_{k_i}{ F_{r_i,k} }\right|^2}
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| {\displaystyle \frac{K}{K-1} \sum_{r_i \in R}
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| \left| \sum_{k_i}F^2_{r_i,k} - \frac{1}{K}\left(\sum_{k_i}F_{r_i,k}\right)^2 \right|}
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| </math> | |
| -->
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| where <math>F_{r_i,k}</math> is the complex structure Factor for image k for a pixel <math>r_i</math> at radius <math>R</math>. It is possible convert the SSNR into an equivalent FRC using the following formula:
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| :<math> | |
| FRC = \frac{SSNR}{SSNR + 1}
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| </math>
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| == See also ==
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| * [[Resolution (electron density)]]
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| * [[Fourier shell correlation]]
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| == Notes ==
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| {{reflist|2}}
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| == References ==
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| <div class="references-small">
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| *{{cite journal
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| | last = Unser
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| | first = M.
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| | coauthors = Trus, B.L.; Steven, A.C.
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| | title = A New Resolution Criterion Based on Spectral Signal-To-Noise Ratios
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| | journal = Ultramicroscopy
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| | volume = 23
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| | issue = 1
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| | pages = 39–51
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| | doi=10.1016/0304-3991(87)90225-7
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| | year = 1987
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| | pmid=3660491}}
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| *{{cite journal
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| | last = Harauz
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| | first = G.
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| | coauthors = M. van Heel
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| | title = Exact filters for general geometry three dimensional reconstruction
| |
| | journal = Optik
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| | volume = 73
| |
| | pages = 146–156
| |
| | year = 1986}}
| |
| *{{cite journal
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| | last = van Heel
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| | first = M.
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| | title = Detection of objects in quantum-noise limited images
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| | journal = Ultramicroscopy
| |
| | volume = 8
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| | pages = 331–342
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| | year = 1982}}
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| *{{cite journal
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| | last = Saxton
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| | first = W.O.
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| | coauthors = W. Baumeister
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| | title = The correlation averaging of a regularly arranged bacterial cell envelope protein
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| | journal = J Microscopy
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| | volume = 127
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| | pages = 127–138
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| | year = 1982
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| | doi=10.1111/j.1365-2818.1982.tb00405.x}}
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| *{{cite journal
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| | last = Böttcher
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| | first = B.
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| | coauthors = Wynne, S.A.; Crowther, R.A.
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| | title = Determination of the fold of the core protein of hepatitis B virus by electron microscopy
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| | journal = Nature
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| | volume = 386
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| | pages = 88–91
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| | doi=10.1038/386088a0
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| | year = 1997
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| | pmid = 9052786
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| | issue = 6620}}
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| *{{cite book
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| | last = Frank
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| | first = Joachim
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| | authorlink = Joachim Frank
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| | title = Three-Dimnsional Electron Microscopy of Macromolecular Assemblies
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| | publisher = [[Oxford University Press]]
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| | location = New York
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| | year = 2006
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| | pages =
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| | isbn = 0-19-518218-9 }}
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| *{{cite journal
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| | title=Fourier shell correlation threshold criteria
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| | journal=Journal of Structural Biology
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| | year= 2005
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| | last= van Heel
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| | first= M.
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| | coauthors = Schatz, M.
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| | volume=151
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| | pages=250–262
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| | doi=10.1016/j.jsb.2005.05.009
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| | pmid=16125414
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| | issue=3 }}
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| </div>
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| [[Category:Applied mathematics]]
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| [[Category:Engineering ratios]]
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| [[Category:Measurement]]
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| [[Category:Microscopes]]
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| {{mathapplied-stub}}
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Nice to meet up with you, my identify is Ricky Nee. What I adore performing is to enjoy golfing and I would in no way give it up. I have generally loved dwelling in Illinois. Booking holiday seasons has been my working day occupation for a while. I am managing and maintaining a web site below: http://www.ceeh.es/includes/src/_notes/nike-air-max-fly.cfm
Feel free to visit my webpage: Nike Air Max 2012