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

**Follow-Ups**:**Re: maximum entropy method for deconvolution***From:*"turnback" <turnback@bluebottle.com>