Level 2 Help for WIENER

The input files to WIENER are:

1. The fourier transform of the image to be restored, in the format
  produced by programs FFT22 or FT2.

2. The optical transfer function (OTF) of the degraded image, i.e.,
  the fourier transform of the point spread function (PSF).  This may
  be obtained using program PSF.

3. Optionally, the fourier transform of the desired output point
  spread function.  Normally one desires a delta function for this,
  and this input is not specified.

All input files must be of COMPLEX format and of the same size.

The output file is the restored fourier transform.  The corresponding
image may be produced using program FFT2 in inverse mode.

The output file will be of the same size as the input.

This parameter specified the signal-to-noise ratio to be used in the
restoration. Noisy images should have values like 5. Clean images
should have values like 30.

The program options:
 VALID=("direct","wiener","ratio","amplitude")  DEFAULT="wiener"

option=wiener (the default)
WIENER applies the Wiener noise additive restoration model on a point
by point basis:
 
        OUT(i,j) = IN(i,j) * W(i,j)
 
                        OTF"(i,j)
        W(i,j) = -----------------------
                 |OTF(i,j)|**2 + 1/SN**2
 
        OTF is normalized by dividing by the dc term.
 
option=direct
Wiener applies the OTF directly to the input:
 
        OUT(i,j)= IN(i,j) * OTF(i,j)
 
        OTF is normalized by dividing by the dc term.
 
option=ratio
Wiener constructs a transfer function from both inputs:
In this mode OTF is a focused image and IN is a blurred image.
 
                        X"(i,j)
        OUT(i,j) = -----------------------
                   |X(i,j)|**2 + 1/SN**2
 
        X(i,j)= IN(i,j)/OTF(i,j)
 
        IN and OTF are normalized by their dc terms
 
        Notice that no corrected image is produced. What you get is the
        fft of the restoring kernel. You may load a small piece into FILTER
        to restore the original image. If you use all of it you'll just
        reproduce OTF.
 
option=amplitude
Wiener constructs a transfer function from both inputs:
In this mode OTF is a focused image and IN is a blurred image.
 
        OUT(i,j)= IN(i,j) * W(i,j)
 
                        X(i,j)
        W(i,j) = -----------------------
                 |X(i,j)|**2 + 1/SN**2
 
        X(i,j)= | IN(i,j) | / | OTF(i,j) +.00001 |
 
        IN and OTF are normalized by their dc terms.
 
        Notice that W is real and symmetric so the convolving kernel will
        also be symmetric. This function cannot correct for phase.
 
where IN and OUT are the fourier transforms before and after restoration
respectively, W is the Wiener filter, OTF is the optical transfer function
(the fourier transform of the point spread function), OTF" is the complex
conjugate of OTF, and SN is the signal-to-noise ratio.