MATLAB: Deconvolution with Lucy-Richardson method

Question

I am trying to deblur an image using MatLab. I have the point spread function (PSF) that the images was blurred with. Furthermore, I know there is noise that is Gaussian distributed, and the signal to noise ratio (SNR) is very high (>20).

Matlab has a couple of deconvolution functions that use direct filtering (regularized filter and Weiner filter), which do not yield satisfactory results.

MatLab has also the Lucy-Richardson (LR) iterative algorithm that, in my case, does a good job in deblurring the image (judged visually).

My question is: is it theoretically sound to use the LR method when the noise in the image has a Gaussian distribution ?

The LR assumes Poisson noise in the blurred image – but does this mean that it performs best with poisson noise, but may also be adequate to use for other types of noise – so I can expect similar results if I want to deblur similar images in the future?

Or does it mean that the LR may randomly yield non-sense results if used for images that have other types of noise than Poisson ?

Answer 1

Well no and yes. Maybe not theoretically the same, however you know, or you should know, that Poisson noise for anything over an expected value of about 8-10 looks virtually identical to Gaussian noise. Just prove it to yourself by doing a Poisson curve for, say 100 and then check the differences between that and a Gaussian fitted to it. The differences will be very small.

And you pretty much never have just 10 photons per pixel unless you are doing very low exposure photon noise limited experiments like in astronomy or radiography. So for most intents and purposes, Poisson noise manifests itself as Gaussian noise, and so the Gaussian noise you have can be considered Poisson noise. The bottom line is how the image looks and if it improves it enough for you to get the required measurements out of it. And it sounds like it's working for you, so go with it.