I would really appreciate a bit of help understanding the whole concept of deconvolution. BTW, I see there was a massive thread 4 years ago, here:

http://www.luminous-landscape.com/forum/index.php?topic=45038, started by Bill. (Which humbles me a bit as I can see you guys have been talking about this for ages!). I've read some of it and while it's very interesting, with something like 18 pages it takes some plowing through! Still, I will get to it.

From a mathematical point of view it seems straightforward enough: the signal f is convolved with another signal g to yield h. If we know g then we can find its inverse and so recover f. If we don’t know g then we can guess it or estimate it and so attempt recovery of f.

Noise messes things up a bit because it’s added to the convolved signal … so how do we remove it from h before doing the deconvolution? Well, one way would be to add some blur to h (in other words convolve it further, which isn’t a brilliant idea if the g was a blur function to start off with!).

Anyway, moving on to imaging, I assume that

**all** filters convolve the image (essentially one function applied to another). If we convolve the image with a blur filter and then apply the inverse filter (a sharpening filter?) then we are convolving the image twice, but the second convolution is also a deconvolution. Is that correct?

Looking at the Ps Custom filter, it’s easy enough to apply a blur and then apply the inverse (so where the adjacent pixel was added, we now subtract it). The effect is to remove the blur … but it also introduces the beloved halo!

So I guess I must be missing something fundamental! Or not using the Ps Custom filter correctly, which is also highly likely!

But assuming that I’m not entirely off the mark, when Jeff says that the Lr sharpen is effectively a USM-type sharpening when used with a low Detail setting, but becomes a deconvolution filter with high Detail settings … I’m both puzzled and lost. I’m puzzled as to how a Detail setting of 0 gives USM (which to my mind is a deconvolution if its intention is to remove blur) while at 100 it’s a deconvolution.

If I take an image and blur it with a Gaussian blur, radius 3, and then sharpen using the ACR sharpen, moving the Detail to 100% certainly gives more sharpening, but it also gives a nice (NOT) halo … it certainly doesn’t recover the image to the pre-blur version.

Here is a very simple test image (real-life) that can be used to try out the different techniques:

http://www.irelandupclose.com/customer/LL/sharpentest.tifI’ve tried various methods (after applying a Gaussian blur of 3) and none of them seem to be particularly effective. I would very interested indeed if you have a filter, or multiple filters, or filter applied multiple times, that can (within reason) restore the image to the original.

And I would be very grateful for clarification on deconvolution (and correction of my understanding, particularly on how it is normally applied to digital images). There's a lot of talk about deconvolution, but I doubt that there are too many of us who understand it (me included)!

Robert