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Often said "you could compute out the camera shake if you knew the blur function"...

One area frequently plagued by shake: Night photography.

One thing frequently found in night photography: Stars or remote lamps which trace out the camera shake almost like an oscillograph, often with either brightness or blooming/flare radius giving an indication of how long the camera was stationary in what exact position.

Can this be used to derive the "blur function", and is there software around that can do this (without resorting to eg matlab and a lot of skill in using it)?

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Yes, this precisely what Photoshop CC's Shake Reduction filter does. Adobe first publicly demonstrated their prototype feature at Adobe Max 2011. The crowd was pretty wowed by the demo. While it was demonstrated in 2011, Piccure actually introduced the feature before Adobe in 2013, as a plugin to Photoshop.

See also: Adobe's help page for the Shake Reduction filter.

One of the better techniques to do this falls under the umbrella term of adaptive deconvolution. An example algorithm is described in the following paper (free to access under CC Attribution license), with interesting result images:

  • Hsin-Che Tsai and Jiunn-Lin Wu, “An Improved Adaptive Deconvolution Algorithm for Single Image Deblurring,” Mathematical Problems in Engineering, vol. 2014, Article ID 658915, 11 pages, 2014. https://doi.org/10.1155/2014/658915.

The tool SmartDeblur uses blind deconvolution, which is a less sophisticated technique to attempt to identify the blur function and remove the blur. It works well enough for some simple cases, but tends to have very visible and undesirable artifacts, such as "halo" ringing.

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