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