RF SN - Spectral SNR of images, resolution determination & integral SNR ||

PURPOSE

Compute the Spectral Signal-to-Noise Ratio (SSNR), its' Variance of a series of images, and integral (across the whole spacial spectrum) Signal-to-Noise Ratio (SNR) of a series of images. Takes real 2D input images. Stores the SSNR data in a document file (spacial frequency, SSNR, number of pixels in each ring, and variance of SSNR). Allows resolution determination by pointing to the frequency at which SSNR falls below a value of 4.0.   Example.

SEE ALSO

FRC	[Fourier ring correlation and resolution determination ||]
RF	[Phase Residual & Fourier ring correlation, 2D ||]
RF 3	[Phase Residual & Fourier shell correlation, 3D ||]

USAGE

.OPERATION: RF SN

.INPUT FILE NAME OR TEMPLATE (E.G. STK@****): IMG***
[Enter template for input images in the set]

If file name has '*' the following question appears:

.FILE NUMBERS OR SELECTION DOC. FILE NAME: 1-700
[Enter file numbers or the name of a document file containing file numbers in the first register column.]

.MASK FILE: MAS999
[Enter the name of mask image used to mask each input image in the set. If you do not want to mask the images, you will have to create a mask image with constant intnsity = 1 using operation 'BL'.]

.RING WIDTH: 0.5
[Enter ring width of each frequency radius for SSNR computation.]

.OUTPUT DOCUMENT FILE: DOC001
[Enter name for resulting document file.]

Reports integral (across the whole spacial spectrum) Signal-to-Noise Ratio (SNR)

NOTES

1. This operation is a good substitute for the Fourier Ring Correlation 'FRC'
   operation for noise estimation and resolution determination.
   

2. Operation calculates the following values:
   SIGNAL(I): Sum of power spectra of all input images over Fourier units in each ring of radius I
   SIGDIF(I): Sum of power spectrum of differences between all input images and average image over
   Fourier units in each ring of radius I
   SSNR(I): Signal-to-Noise Ratio in each ring of radius I, calculated as
   SSNR(I) = SIGNAL(I)/SIGDIF(I) - 1 ( SSNR(I) = 0 if SSNR(I) <= 1 )
   VAR(I): the expected variance of SSNR(I), calculated as
   VAR(I) = SQRT { (2 + 4*SSNR(I))/M +
   + [2 + 4*SSNR(I) + 2*SSNR(I)**2]/[M*(N(I)-1)] }
      --- M = number of images
      --- N(I) = number of Fourier units for each ring of radius I.
   

3. In SSNR calculation SIGDIF(I) is divided by the number of images to reflect the
   statistical reliability of averaged image, and in integral SNR calculation SIGDIF(I) is
   not divided (it's similar to relation between standard error and standard deviation of
   the mean in statistics)
   

4. Document file contents:
   

   KEY = RING RADIUS

   RING RADIUS (NORMALIZED SCALE)

   SSNR(I)

   NVALS(I)

   VAR(I)

   where RING RADIUS - Normalized spacial frequency (0.5 corresponds to Nyquist frequency)
   SSNR - Signal-to-Noise Ratio in each ring of radius I as
   NVALS - Number of pixels in ring
   VAR - SSNR variance
   

5. References:
   [a] M. Unser, B.L. Trus & A.C. Steven, Ultramicroscopy 23(1987) 39-52: "A New Resolution Criterion Based on Spectral Signal-to-Noise Ratios"
   [b] M. Unser, B.L.Trus & A.C. Steven, Ultramicroscopy 30(1989) 429-434: "The Spectral Signal-to-Noise Ratio Resolution Criterion: Computational Efficiency and Statistical Precision"
   [c] M. Unser, C.O.S. Sorzanoa, P Thévenaz, S. Jonic, C. El-Bez, S. De Carlo, J.F.Conway & B.L. Trus, J Struct Biol. 149(2005) 243-255: "Spectral Signal-to-Noise Ratio and Resolution Assessment of 3D reconstructions"
   d

SUBROUTINES

SSNRB

CALLER

FOUR1