> 1) This has anything to do with complex numbers, even if you use the FFT 
> method to recover the source image.

Agreed, I incorrectly thought that if you had some complex version of the 
resultant you would have more information to regenerate the source, but with 
real source image and real kernel that is obviously not possible.

> 2) This prevents you from getting an approximate answer in practice.

> >>>>>> result:
>
> {3 3 3 3 3 3 3 3}
>
> cyclic-source: {3 3 3 3 3 3 3 3}
>
> zero-source: {5.3333, 1.3333, 4.0000, 2.6667, 2.6667, 4.0000, 1.3333, 
> 5.3333}
>
> full-intensity-source: {4.5556, 1.8889, 3.6667, 2.7778, 2.7778, 3.6667, 
> 1.8889, 4.5556}

My point was that the following are all valid solutions to the source image:

{3,3,3,3,3,3,3,3}
{2,4,2,4,2,4,2,4}
{1,5,1,5,1,5,1,5}
{6,0,6,0,6,0,6,0}

In this case even the centre pixels could be anywhere from 0 to 6, and the 
"appearance" of the image is radically different in each case.  Surely this 
is exactly the sort of detail a "deblurring" filter needs to recover, but it 
seems impossible.

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