% @(#)grad_wave.hlq	17.1.1.1 (ESO-IPG) 01/25/02 17:21:09
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%.COPYRIGHT  (c)  1993 European Southern Observatory
%.IDENT      grad_wave.hlq
%.AUTHOR     18-MAY-93, IPG/ESO
%.KEYWORDS   MIDAS, help files, 
%.PURPOSE    On-line help file for the command: GRAD/WAVE
%.VERSION    1.0  JS : Creation, 18-MAY-93
%----------------------------------------------------------------
\se
SECTION./WAVE
\es\co
GRAD/WAVE					   JS  18-MAY-93
\oc\su
GRAD/WAVE Image_In Psf Imag_Out [residual] [Nb_Scales]
          [N_Sigma, Noise] [Epsilon] [Max_Iter] 
\us\pu
Purpose:    
         Deconvolution by the one step gradient method  with a 
         regularization in the wavelet space. The deconvolution equation is:\\
                                I = P * O + B\\
         where I is the data, P is the PSF, B is the noise, and O the object
\up\sy
Syntax:     
         GRAD/WAVE Image_In Psf Imag_Out [residual] [Nb_Scales]
                   [N_Sigma, Noise] [Epsilon] [Max_Iter]
\ys\pa
         Image_In =   name of the input image
\ap\pa
         Psf =        name of the Point Spread Function P
\ap\pa
         Imag_Out =   name of the deconvolved image output image
\ap\pa
         residual =   name of the file wich will contain the residual \\
                      I - P * O\\  
                      default value is "residual.bdf"       
\ap\pa
          Nbr_Scale = Number of scales of the wavelet transform; default is 4.
\ap\pa
          N_Sigma =   threshold parameter level_j at a scale j of the wavelet 
                      transform:\\
                         Level_j = N_Sigma * Noise_Standard_Deviation_Scale_j\\
                      The standard deviation of the noise at the scale j is
                      estimated from the noise standard deviation of the image
                      N_Sigma = 4 is the default value.
\ap\pa
          Sigma_Noise = Standard deviation of the noise.
                      If Sigma_Noise = 0. then the standard deviation
                      of the noise is estimated in the program.
                      The default value is 0.
\ap\pa
          Epsilon =   Convergence parameter; default value is 0.001
\ap\pa 
          Max_Iter =  maximum number of iterations; default value is 100
\ap\see
See also: 
            TRANSF/WAVE, FILTER/WAVE, LUCY/WAVE, CITTERT/WAVE
\ees\no
Note:       
            none
\on\exs
Examples:
\ex
            GRAD/WAVE   data psf result
            deconvolves the frame data by the psf and stores the
            deconvolved image in result. 
\xe\ex
            GRAD/WAVE data psf result ? ? 3.5,50 ? 300 
            the standard deviation of the noise is 50, and the threshold
            level at the scale j is: 3.5 * Standard_deviation_Scale_j
            the maximum number of iterations is 300. But the program can
            stop before (because of the convergence parameter).
\xe\ex
            GRAD/WAVE data psf result ? ? ? 0. 50
            sets the convergence paramater to zero, and the number of
            iterations to 50. In this case, 50 fifty iterations will be 
            done.
\xe\sxe