On 3 Apr., "Terry Duell" <[email protected]> wrote:

> Applying the psf to the blurred still doesn't give back a result even
> close to the sharp, so there are probably other things not right with what
> I am doing. A bit more homework to do.

Hang on, I don't think convolving the blurred image with the PSF will
recover the original - it will worsen the blur. You have to revert the
process (forgive me if I'm stating the obvious and you're doing just
that), I just can't think of what you have to do to the kernel to use
it to revert the convolution (maths buffs please come to the rescue!).
Of course that bit may be easier in the frequency domain.

And I still believe those sharp discontinuities and minimum-to-maximum
jumps in your source image may be part of the problem, never mind you
can recover the source image precisely.

> All the thorny issues involved with 'real' images  
> are looking like more than I can handle.

You have my sympathy. I feel like I've been in precisely your position
quite often when the maths is getting heavy. This is why I prefer the
convolution in the 'time' domain (btw. where is time in a 2D
matrix ;-) - after all, convolution is nothing than taking a few
copies of the original image, multiplying them with a factor, shifting
them a bit in various directions and adding them up. I always found it
miracoulous how you could achieve similar stuff in the frequency
domain, and I never really got my head round complex exponentials
either when I tried to understand the FT on an 'intuitive' level, even
though complex exponentials do precisely the same as sines and
cosines, and much cleaner and faster...

Dabbling with real-world images and running up against my mathematical
limits always made me respect the maths that actually did work on
those images much more - stuff like SIFT and SURF, gaussians and
laplacians and what not...

Kay

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