Help for WNRM2005

This program modifies a fourier transform using the Wiener noise additive
model for restoration.  The Wiener algorithm is similar to that 
provided in WIENER and WNR2005, but has been modified to match a
MATLAB script.

The inputs can now have a real matrix that gives a per-pixel signal to
noise ratio (SN) in place of the constant snr given by the parameter.
EXECUTION:
  WNRM2005  INP=(in,otf,snr)  OUT

 where:  in is the fft of the input degraded image.

         otf is the optical transfer function. This represents the image
             degradation. It is also an fft the same size as in.

         snr  is the signal/noise ratio image (real format) to be applied..
                It is optional.

         out is the fft of the output image.

Note that WNRM2005 has no SIZE parameter.  The output must be the same
size as the primary input, and the other input files must also be of
the same size.

METHOD

WNRM2005 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 should be pre-normalized by using FFT2005 'norm option.

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.

EXAMPLE

Generate OTF from PSF
fft2005      amt_psf_pan.rel amt_OTF.cmp mode=forward format=comp               insect=(3375,3648) 'quadswap 'norm 'preqswap
Convert snr psf to zero-filled fft, then convert to real*4 image
fft2005      amt_snr_pan_high.rel xxtmp3 mode=forward format=comp               insect=(3375,3648) 'quadswap 'preqswap
f2comp       xxtmp3 xxtmp4 size=(1,1,3375,3648) op=cabs
Convert Image to FFT
fft2005      amt_snap_pan.rel xxtmp1 'forward 'comp
Apply weiner filter
wnrm2005    (xxtmp1,amt_OTF.cmp,xxtmp4) xxtmp2 'snrimg
Convert back to image dimensions
fft2005      xxtmp2 newimage.hlf mode=inverse format=half


SIMULATION

The operation of WNRM2005 could be replaced with the following
vicar steps, but wnrm2005 is faster, and has less rounding errors.
(Reference preceeding example)

wnrm2005    (xxtmp1,amt_OTF.cmp,xxtmp4) xxtmp2 'snrimg

  equals:   (except for rounding errors)

f2comp       amt_OTF.cmp xxtmp6 'conj
f2comp       amt_OTF.cmp xxtmp7 'cabs
f2          (xxtmp7,xxtmp4) xxtmp8 func="((in1**2)+(1/in2/in2))"
f2comp      (xxtmp6,xxtmp8) xxtmp9 'div 'scalar
qswp2005     xxtmp9 xxtmp7 'reverse
f2comp      (xxtmp1,xxtmp7) xxtmp2 'mult

HISTORY

  
  Sep 2007 A Zobrist  NSR input image inverted to SNR input

  Nov 2007 P Kim wnrm2005 program is a spinoff from wnrm2005 to
                 simulate matlab results for Joe Green  

 Current Cognizant Programmer:  P Kim, A Zobrist
 Revisions:
Thu Jan  3 2008 wlb switched to USES_ANSI_C AND LIB_CARTO; misc cleanup  
2022-07-27 B. Crocco afids to opensource (untested)

PARAMETERS: