% @(#)citterwave.hlq	19.1 (ESO-IPG) 02/25/03 13:34:18
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%.COPYRIGHT  (c)  1993 European Southern Observatory
%.IDENT      citterwave.hlq
%.AUTHOR     18-MAY-93, IPG/ESO
%.KEYWORDS   MIDAS, help files, 
%.PURPOSE    On-line help file for the command: CITTERT/WAVE
%.VERSION    1.0  JS : Creation, 18-MAY-93
%----------------------------------------------------------------
\se
SECTION./WAVE
\es\co
CITTERT/WAVE					   JS  18-MAY-93
\oc\su
CITTERT/WAVE  Image_In Psf Imag_Out [residual] [Nb_Scales, Max_Iter]
               [N_Sigma, Noise] [Epsilon] [Fwmh]
\us\pu
Purpose:    
            Deconvolution by Van Cittert's algorithm 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 nopise and O is the 
            object to determine
\up\sy
Syntax:     
          CITTERT/WAVE Image_In Psf Imag_Out [residual] [Nb_Scales, Max_Iter]
                       [N_Sigma, Noise] [Epsilon] [Fwhm]
\ys\pa
          Image_In = Name of the image I
\ap\pa
          Psf =      Name of the Point Spread Function P
\ap\pa
          Imag_Out = Name of the deconvolved image O
\ap\pa
          residual = Name of the file wich will contain the residual
                      residual = I - P * O\\  
                      default value is "residual.bdf"       
\ap\ap
          Nbr_Scale = Number of scales of the wavelet transform; default 4.
\ap\pa
          Max_Iter = maximum number of iterations; The default value is 100
\ap\pa
          N_Sigma =  threshold parameter
                     The threshold 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
          Fwhm =     Full Width at Half Maximum. This parameter allows us to 
                     reduce the resolution in the deconvolved image. If 
                     Fwhm is greater than 0. then the resolution is limited 
                     the image of a star will be Gaussian with a a full width 
                     at half maximum equal to Fwmh. 
\ap\see
See also: 
          TRANSF/WAVE, FILTER/WAVE, LUCY/WAVE, GRAD/WAVE
\ees\no
Note:       
          none
\on\exs
Examples:
\ex
            CITTERT/WAVE  data psf result
            deconvolves the frame data by the psf and stores the
            deconvolved image in result. 
\xe\ex
            CITTERT/WAVE data psf result ? 4,300 3.5,50  
            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, due to the convergence parameter. 4 scales are
            used in the wavelet transform.
\xe\ex
            CITTERT/WAVE data psf result ? 4,50 ? 0. 3.
            set the convergence paramater to zero, and the number of
            iterations to 50. In this case, 50 fifty iterations will be 
            done. The Full Width at Half Maximum is equal to 3.
\xe\sxe



