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Fair use rationale for Image:Wiki reconstruct.png

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Image:Wiki reconstruct.png is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in this Wikipedia article constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

Please go to the image description page and edit it to include a fair use rationale. Using one of the templates at Wikipedia:Fair use rationale guideline is an easy way to insure that your image is in compliance with Wikipedia policy, but remember that you must complete the template. Do not simply insert a blank template on an image page.

If there is other fair use media, consider checking that you have specified the fair use rationale on the other images used on this page. Note that any fair use images uploaded after 4 May, 2006, and lacking such an explanation will be deleted one week after they have been uploaded, as described on criteria for speedy deletion. If you have any questions please ask them at the Media copyright questions page. Thank you.

BetacommandBot (talk) 05:39, 30 November 2007 (UTC)[reply]

3 to the fourth power is not 729. 3 to the fourth is 81, and 3 to the sixth is 729. Which one was intended?

Fixed points and solution set

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I've commented out the following statement:

The set of fixed points in a particular application will normally have a large dimension, even when the solution set is a single point.

The iterated map is xx + β S, where S is the difference between the two projections PA(fB(x)), which is an element of A, and PB(fA(x)), an element of B. We see that x is a fixed point of the map iff S = 0, which means that PA(fB(x)) = PB(fA(x)), so this is a common point of A and B. Then, furthermore, PA(x) = x, so fA(x) = PA(x) − (PA(x)−x)/β = x. Likewise, PB(x) = x. So the common point in the intersection of A and B is x itself. This shows that x is a fixed point iff it is in the solution set of xAB. The set of fixed points and the solution set coincide, so one cannot have a larger dimension than the other.  --Lambiam 22:10, 10 December 2012 (UTC)[reply]


Phase Retrieval Section

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I restored this section because the algorithm's origins can be traced to this particular application. Also, the reconstruction figure now has the necessary explanatory text.  --Veit Elser 10:42, 23 January 2014 (UTC)[reply]