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MathGroup Archive 2007

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Re: maximum entropy method for deconvolution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75417] Re: maximum entropy method for deconvolution
  • From: Guillermo Sanchez <guillermo.sanchez at hotmail.com>
  • Date: Sun, 29 Apr 2007 03:11:16 -0400 (EDT)
  • References: <f0v6f3$929$1@smc.vnet.net>

The book Applied Mathematica by W.T. Shawn and J.Tigg includes on
example about the MEM.
You can also download one notebook from my web side http://web.usal.es/guillermo
-> Modeling and Simultion

Cheers

Guillermo

On 28 abr, 12:08, dantimatter <dantimat... at gmail.com> wrote:
> 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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