How does radius of point spread function affect reconstruction errors?

[cp05]

Hi guys,
I've been struggling with this concept for a few days now.
I have this *good* image that I am blurring (using a gaussian blur), then adding some small percentage of gaussian white noise to it. Then from that image, I want to compute the naive solution (just assuming B=AX and solving for X...where B is the blurred image I created and X is the *good* image, with A being the matrix that takes into account this gaussian point spread function).

I have a handy dandy textbook that says that if I use periodic boundary conditions (which I am), then I can just use the point spread function and don't ever have to construct A (yay!). I do this by computing the eigenvalues of A using fast Fourier transforms (not sure how those work either...but I guess that's a different question for a different time), then using the inverse fast Fourier transform to solve for X using the blurred matrix and those eigenvalues of A.

All great!

By playing around with the radius of my gaussian blur...I notice that at larger gaussian blur radii (ad same % of white noise), my resulting naive X solution has a lot more noise! So I was wondering if anyone can help me figure out why this happens. Why am I getting more noise in my solution with larger radii of blur...because I am not changing the % of white noise at all!

If someone could help, or point me in the right direction, I would be ever grateful.
Thanks!

 

[Drakkith]

Random guess, but wouldn't the larger blur mean less SNR per pixel and more total noise that is added to each calculation since you have the PSF spread over more pixels?
(I hope that makes sense. My only knowledge of this subject comes from my astrophotography)