Talk:Deconvolution

History needs expansion
Some online research (eg his obituary) indicates that A. Lindo Patterson was another colleague of Wiener's involved in the application of the concepts of (de)convolution. He was working in X-ray crystallography, probably at the same time or earlier than Robinson's work in seismology. Any information on this topic would be appreciated. This article needs broader information on the history of deconvolution, especially outside of seismology (my own bias). Gwimpey 21:50, 10 April 2006 (UTC)

Deconvolution and NMR
I've seen several references to deconvolution in reference to Nuclear magnetic resonance. Someone with some knowledge on the topic might want to add a little info. --Tsuji 00:23, 17 August 2006 (UTC) ---

New software link
This software is mainly developed for astronomical image processing:
 * SImg (GPL'd software) —Preceding unsigned comment added by 217.114.211.20 (talk) 17:46, 27 January 2008 (UTC)

Since version 8, Mathematica provides two, fairly comprehensive commands for deconvolution. I like to add external links to their reference pages:
 * ImageDeconvolve,
 * ListDeconvolve. 84.61.173.24 (talk) 19:38, 21 December 2010 (UTC)

Nice example using Richardson-Lucy adaptive restoration
Clarkvision_com Saturn Photo Gallery 1

His homepage says: All images, text and data on this site are copyrighted. They may not be used except by written permission from Roger N. Clark. All rights reserved. - perhaps I shouldn't have copied that - oops!

Do you think it would be worth asking for permission to use his images ? Or at least link there ? He seems quite an authoritative source IMO - FWIW. --195.137.93.171 (talk) 02:16, 7 March 2008 (UTC)

reqdiagram
What kind of diagram is required? Please re-add this template with more details about what is wanted. thanks --pfctdayelise (talk) 12:18, 27 July 2008 (UTC)

Is "s(t) = e(t) * w(t)" correct?
I'm not an expert in this field, but I think "s(t) = e(t) * w(t)" is incorrect, as it is the functions that are convoluted, not the function values. IMHO the equation should be replaced by "s(t) = e*w(t)" or possibly "s(t) = (e*w)(t)". Dendropithecus (talk) 18:54, 9 February 2009 (UTC)

statistics of distributions
In general if you have a random variable Z that is a sum of two random variables X and Y, the probability density function of the distribution of Z will be the convolution of those of the distributions of X and Y. I have seen references to using deconvolution to estimate the distribution of the components from the distribution of their sum (and presumably either the exact or estimated distribution of the other components, or some assumptions about their nature.) Unfortunately I don't know enough about the subject to write any useful encyclopedic information about it. 200.125.112.113 (talk) 18:35, 16 July 2009 (UTC)

Shareware added
Hi folks, I added a link to shareware for image deblurring that I recently released. Hope its ok for you. In other case, please contact me to discuss it. Filip —Preceding unsigned comment added by 78.45.58.52 (talk) 18:37, 20 December 2009 (UTC)

Inverse identification
Deconvolution is used to identify the inverse transfer function of a plant and use the obtained model to drive the plant (to control). See "Adaptive iverse control", Bernard Widrow, 1993. - 81.180.223.197 (talk) 08:18, 9 July 2011 (UTC)

About merger with blind deconvolution
There is a proposal of merger between blind deconvolution and deconvolution.

I disagree with this. Although the name blind deconvolution suggests that it is merely a special case of deconvolution, it is not. Convolution and deconvolution are well-defined mathematical operations while blind deconvolution is an entirely different story.

First of all, it is not well-defined (there is no "correct answer") hence it does not belong to the field of mathematics, but rather in applied mathematics. Blind deconvolution is subjective while deconvolution is objective.

Secondly, blind deconvolution is an area of active research where progress is still being made (in contrast to convolution/deconvolution which are "just algorithms"). The methods used in blind deconvolution are highly dependent on their underlying applications and there is much to be said about the different methods used. — Preceding unsigned comment added by 130.238.58.207 (talk) 18:39, 15 October 2013 (UTC)

One could argue that all mathematics is the study of groups and their symmetries. Except for the math Ph.D. amongst us this broad scope classification provides little clarification or insight. Blind deconvolution is often overlooked as a possibility for achieving an inexact yet useful solution to a problem. The art/insight required to pick a practical basis set for reasonable closed form computation is both at the heart of the best mathematics and divergent from the purists who would desire an exact yet non-computable solution. If the purpose of Wiki is to educate and be useful, then the useful technique of blind deconvolution deserves its own place. To argue that it should be buried in deconvolution in general is to argue that we should merge cosmology into the grand unified theory of space time which subsequently gets merged into the theory of super symmetric Lie groups. Yes I came back to groups again.

A separate entry for Blind deconvolution allows more people to easily access valuable information and in some degree also more easily allows its in-exact/artful nature to be exposed. I would recommend not merging into the general deconvolution topic. Nothing wrong with cross reference between the two of course. - 139.137.128.43 (talk) 18:29, 2 July 2014 (UTC)

Deconvolution is a general topic in mathematics. Blind deconvolution is one of many different numerical methods used to try to solve convolution problems. They are not appropriate to merge. Cecoppola (talk) 03:39, 16 May 2016 (UTC)

Example of convolution, seen frequently
When in a dark room with a brightly-lit scene outside, if there is an aperture (like a hole in a opaque curtain, or the triangular small gap if the curtains are not completely closed), an inverted and reversed image of the outside scene may be seen as splotches of coloured light on the walls of the dark room. This is a large-aperture version of the pinhole camera.

It is fuzzy because each point source of light in the outside scene produces its own (e.g.) triangular patch of light on the inner wall - that shape and size is the function g in the above f * g = h (corresponding to the transfer function of an instrument).

A clear image of the outside scene can be recovered from a photograph of this fuzzy image on the internal wall, by deconvolution, using the shape, dimensions and orientation of the hole in the curtains. {I am 77yo and want another physicist to check this} davd (talk) 18:34, 10 January 2014 (UTC)
 * AIUI the problem with the large pinhole is it's essentially a form of spacial lowpass filter, so when you invert it you end up with very high gain on the components with high spacial frequency and that leads to a noisy reconstruction. 151.229.191.223 (talk) 03:07, 22 June 2014 (UTC)

linearity
It seems to me that the article should separate, and mention the difference between, linear and non-linear deconvolution. Dividing the Fourier transforms is linear. This is well described in Jansson's Deconvolution of Images and Spectra, Second Edition. It adds the restriction that intensity can't go negative, and often works much better in signals with noise (all of them). Gah4 (talk) 21:52, 6 November 2020 (UTC)