Name

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MAX_ENTROPY

Purpose

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Deconvolution of data by Maximum Entropy analysis, given the PSF

Explanation

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Deconvolution of data by Maximum Entropy analysis, given the
instrument point spread response function (spatially invariant psf).
Data can be an observed image or spectrum, result is always positive.
Default is convolutions using FFT (faster when image size = power of 2).

Calling Sequence

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for i=1,Niter do begin
Max_Entropy, image_data, psf, image_deconv, multipliers, FT_PSF=psf_ft

Inputs

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data = observed image or spectrum, should be mostly positive,
with mean sky (background) near zero.
psf = Point Spread Function of instrument (response to point source,
must sum to unity).
deconv = result of previous call to Max_Entropy,
multipliers = the Lagrange multipliers of max.entropy theory
(on first call, set = 0, giving flat first result).

Outputs

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deconv = deconvolution result of one more iteration by Max_Entropy.
multipliers = the Lagrange multipliers saved for next iteration.

Optional Input Keywords

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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.
      /LINEAR switches to Linear convergence mode, much slower than the
default Logarithmic convergence mode.
LOGMIN = minimum value constraint for taking Logarithms (default=1.e-9).

External Calls

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function convolve( image, psf ) for convolutions using FFT or otherwise.

Method

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Iteration with PSF to maximize entropy of solution image with
constraint that the solution convolved with PSF fits data image.
Based on paper by Hollis, Dorband, Yusef-Zadeh, Ap.J. Feb.1992,
which refers to Agmon, Alhassid, Levine, J.Comp.Phys. 1979.
      A more elaborate image deconvolution program using maximum entropy is
      available at
      http://sohowww.nascom.nasa.gov/solarsoft/gen/idl/image/image_deconvolve.pro

History

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written by Frank Varosi at NASA/GSFC, 1992.
Converted to IDL V5.0 W. Landsman September 1997