Re: Re: maximum entropy method for deconvolution
- To: mathgroup at smc.vnet.net
- Subject: [mg75489] Re: [mg75469] Re: maximum entropy method for deconvolution
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Thu, 3 May 2007 03:40:15 -0400 (EDT)
- References: <200704281000.GAA09123@smc.vnet.net><email@example.com> <200705020749.DAA04907@smc.vnet.net>
On May 2, 2007, at 3:49 AM, dantimatter wrote:
> Thanks to all for the help, and a special thanks to Guillermo Sanchez
> for the Modeling and Simulation notebook. I'm finding that my answer
> is still 'unpleasant'.
I'm not sure what you mean by unpleasant.
> Could it be that the convolution of a function
> with a step-function is something that simply cannot be deconvolved?
In general, yes.
> That perhaps there's information lost in the convolution and it could
> never be recovered?
Yes because the spectrum of a step function is sinc function which of
course means you're multiplying by 0 in the frequency domain at the
nodes of the sinc.
There are approximate methods for this problem since it's equivalent
to finding a "good" pseudoinverse to a singular Toeplitz matrix See
http://www.math.ucdavis.edu/~strohmer/papers/1995/str1695.html for a
case in which the inverse can be found.
If you ever stumble on a good solution for a non-bandwidth limited
signal please let me know.
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