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Re: maximum entropy method for deconvolution

• To: mathgroup at smc.vnet.net
• Subject: [mg75420] Re: maximum entropy method for deconvolution
• From: Roman <rschmied at gmail.com>
• Date: Sun, 29 Apr 2007 03:12:51 -0400 (EDT)
• References: <f0v6f3$929$1@smc.vnet.net>

Dan,
Here's a list of books:

http://www.amazon.de/s?ie=UTF8&index=books-de-intl-us&field-keywords=Maximum%20entropy%20method&page=1

I had used the one named "Maximum Entropy in Action", but took quite
some time to implement something even vaguely correct. I had found all
explanations quite opaque. About a year ago I searched for quite a
while for a free implementation of MEM, but could not find any. I'll
think about how to do your problem, since I guess it is of very
general interest. One of the central parts is the question on how to
define the entropy of the resulting F. I imagine you could use
something of the sort of

S = Integrate[-F(w)*Log(F(w)), {w,-Inf,Inf}]

More later, now it's off to the mountains for some hiking.
Roman.

On Apr 28, 12:08 pm, 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