I am trying to implement a low pass Wiener filter using the mean- squared method, to provide elimination of noisy areas, background texture smoothing, and contrast enhancement. The algorithm I'm using is (to produce output image Q from input image P), to evaluate a 3x3 neighbourhood for each pixel, and Q(x,y) = mu + [ (sigmasquared - nusquared)/sigmasquared ] ( P (x,y) - mu ) Where: mu is the local mean across the neighbourhood sigmasquared is the variance of the 3x3 neighbourhood nusquared is the estimated local variance Now, I don't know the source of the putative high frequency noise, so I have to estimate nusquared, which is where I am running into problems. All the code I can find on the net estimates nusquared by using the variance of the whole of the original image. Not a canonical source I know, but see, e.g., the bottom of: http://www.vislab.uq.edu.au/education/sc3/2000/xinghe/project/theory.html Now this doesn't work for me, as in images to which noise has NOT been added, the local variance is consistently SMALLER than the image variance (in one test image it is never larger than image variance. This seems to me bound to be the case on (for example) an image that has been enlarged by bicubic interpolation and thus is already "smooth". The problem here is that the Wiener filter does terrible things to the image because the term in square brackets goes substantially negative (as sigmasquared << nusquared), causing the output to wildly oscillate. I think the problem here is that all the code examples I have found have assumed that the image variance is a good estimate for the local variance. That's true if you are doing a compsci project where the input image has had a lot of noise added to it, but isn't universally true. I think the problem is that I need a better estimate for nusquared. What would you recommend here? Taking the mean of the 3x3 variances across the image? Alex

# Wiener filtering using mean-squared method: variance problem

Started by ●December 22, 2008