maximum entropy method for deconvolution

• To: mathgroup at smc.vnet.net
• Subject: [mg75403] maximum entropy method for deconvolution
• From: dantimatter <dantimatter at gmail.com>
• Date: Sat, 28 Apr 2007 06:00:08 -0400 (EDT)

```hello all,

first off, many thanks to 'Roman' et al for all the previous help with
my inversion problem.

i have a convolution function G which is the convolution of F and p (G
= F**p).   i know G and i know p, and i'd like to extract F.  i can do
this by taking the Fourier transform of G, dividing by the Fourier
transform of p, and inverting the result to get F.  the problem is
that p is a step function (p = UnitStep[t]*UnitStep[33.6-t]) which has
a lot of zeros in frequency space, and thus  it is difficult to get at
F via inversion.  Mathematica is happily doing the inversion but the
results are very noticeably wrong.

i understand from my conversations with some of you and much time
spent in the library that this is in general a difficult problem, but
there are some methods that are known to make this type of problem
tractable, such as the maximum entropy method (MEM) for inversion.  is
anyone aware of an implementation of a MEM algorithm in Mathematica?
i have read Numerical Recipes a couple of times and i am unable to get
my head around the relevant chapter.  If there isn't a Mathematica
implementation, perhaps someone could offer some advice on where else
to look?  if it exists, a "for dummies" type book with step-by-step
instructions would be the best resource for me...

cheers,
dan

```

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