MAX_LIKELIHOOD

       Maximum likelihood deconvolution of an image or a spectrum.

       Deconvolution of an observed image (or spectrum) given the
       instrument point spread response function (spatially invariant psf).
       Performs iteration based on the Maximum Likelihood solution for
       the restoration of a blurred image (or spectrum) with additive noise.
       Maximum Likelihood formulation can assume Poisson noise statistics
       or Gaussian additive noise, yielding two types of iteration.

       for i=1,Niter do Max_Likelihood, data, psf, deconv, FT_PSF=psf_ft

       data = observed image or spectrum, should be mostly positive,
                               with mean sky (background) near zero.
       psf = Point Spread Function of the observing instrument,
                               (response to a point source, must sum to unity).

       deconv = as input: the result of previous call to Max_Likelihood,
               (initial guess on first call, default = average of data),
               as output: result of one more iteration by Max_Likelihood.
       Re_conv = (optional) the current deconv image reconvolved with PSF
               for use in next iteration and to check convergence.

      /GAUSSIAN causes max-likelihood iteration for Gaussian additive noise
               to be used,  otherwise the default is Poisson statistics.
       FT_PSF = passes (out/in) the Fourier transform of the PSF,
               so that it can be reused for the next time procedure is called,
      /NO_FT overrides the use of FFT, using the IDL function convol() instead.
       POSITIVITY_EPS = value of epsilon passed to function positivity,
                       default = -1 which means no action (identity).
       UNDERFLOW_ZERO = cutoff to consider as zero, if numbers less than this.

       function convolve( image, psf ) for convolutions using FFT or otherwise.
       function positivity( image, EPS= ) to make image positive.

       Maximum Likelihood solution is a fixed point of an iterative eq.
       (derived by setting partial derivatives of Log(Likelihood) to zero).
       Poisson noise case was derived by Richardson(1972) & Lucy(1974).
       Gaussian noise case is similar with subtraction instead of division.

       written: Frank Varosi at NASA/GSFC, 1992.
       F.V. 1993, added optional arg. Re_conv (to avoid doing it twice).
       Converted to IDL V5.0   W. Landsman   September 1997

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