Comments on: Image deblurring – Wiener filter

By: Steve

Steve — Wed, 27 May 2009 18:27:22 +0000

Umar—I’m not an expert on this subject, but I’m only aware of fairly ad hoc methods for estimating noise levels in an image. For example, you could compute the pixel value variance for a subset of image pixels that are considered to be in “smooth” regions, for some suitable definition of smooth.

By: Steve

Steve — Wed, 27 May 2009 18:25:44 +0000

Meng-cian—1. I’ll leave it to you to work out the math on that one, or you can ask one of your instructors. 2. I’m going from a very old memory here, so you’ll need to verify this, but I believe that form of autocorrelation model comes from the assumption that the signal can be approximated by a first-order autoregressive model. You might be able to find more information in a reference on spectrum analysis.

By: Steve

Steve — Wed, 27 May 2009 18:19:16 +0000

Ali—Wiener filtering simplifies to a pure inverse filter when you assume there is no noise. In the presence of noise, a pure inverse filter will tend to greatly amplify any noise present, often making the result unusable.

By: Steve

Steve — Wed, 27 May 2009 18:12:25 +0000

Assaf—Image autocorrelation is related to the image power spectrum, so you can probably use FFTs to speed up the calculation. This is a topic you can probably find in a book on multidimensional digital signal processing.

By: Umar

Umar — Sun, 24 May 2009 20:10:04 +0000

Hi.
I found a paper on fingerprint enhancement. In that paper there was Wiener filter with formula given as

w(n1,n2)= u+((s-v)/s)*(I(n1,n2)-u)

where:
v = noise variance
s = local variance
u = local mean
I = grey-level intensity

and everything is for 3×3 neighbourhood.

i’ve found everything else but don’t know how to find out v(noise variance).
Please help in this regard.
Thanks in advance

By: meng-cian

meng-cian — Thu, 14 May 2009 07:38:12 +0000

1.The minimizer of this expression is given by
G(k,l)=H(k,l)/(H(k,l)^2+S_u(k,l)/S_x(k,l))

2.A common model for the image autocorrelation function is
sigma_x*rho.^sqrt(m^2+n^2) + mean_x^2

I am astudent,
I Did not know how it does come,
Ask how to infer this formula?

By: ratnakar

ratnakar — Tue, 12 May 2009 11:35:35 +0000

Hi, i have some images which are blurred due to circular motion. The different images with angular speed are given.
Can any one help me in removing the blur ??

By: ali

ali — Thu, 07 May 2009 09:21:58 +0000

what does the different between inverse filter and wiener filter ?

By: Assaf

Assaf — Fri, 24 Apr 2009 11:02:00 +0000

Hi,
I have a question regarding the calculations of image autocorrelation function, in our example:

cam_r = circshift(cam,[1 0]);
cam_c = circshift(cam,[0 1]);
rho_mat = corrcoef([cam(:); cam(:)],[cam_r(:); cam_c(:)])
rho = rho_mat(1,2);
[rr,cc] = ndgrid([-128:127],[-128:127]);

is there an easier way o calculate the rho? i have explored the corrcoef() function and it invloves many calculations… can i calculate in another, easier way?
thx

By: Stan Reeves

Stan Reeves — Wed, 08 Apr 2009 21:39:55 +0000

Bob–—The Wiener filter introduces bias into the solution to reduce the noise variance. Essentially, it allows for a small amount of well-defined blurring to smooth the noise while still restoring the image. Thus, impulsive signals like stars will be spread out somewhat and lose their original amplitude.

You can calculate the effective PSF of the blurring followed by Wiener filter and then infer the height of an impulse that has been blurred by this PSF just by comparing the PSF height to the height of the “bump” caused by the star. However, this still won’t recover the original radiometric intensity unless you either know or can estimate the original radius of the star. As you probably know better than I do, if the resolution is fairly limited, you won’t be able to tell the difference between a tiny but bright star and a larger but dim one—especially if the star size is smaller than a pixel in the image plane.