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Regarding my question about Gaussian noise reduction, I would like to know of a simple method to quantify the success of a noise reduction filter.

I've attempted a few methods of noise reduction and I want some method to determine which one works best. I have the original image, a noisy version and a few versions created from attempts to reduce the noise. I thought about trying some matrix distance measurement from the enhanced image and the original image, in order to compare the methods of noise reduction. Will this work okay or is there some other common method other than just looking at the pictures?

Community
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shwartz
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    You will need to be aware that filtering your noisy image will reduce the noise, but it will also modify the underlying image itself. So when you then perform comparisons, you will be quantifying two separate effects. – Oliver Charlesworth Dec 24 '11 at 20:16
  • @OliCharlesworth That's true, but I want to know how far the denoised image is from the original noise-less image. I suppose using the sum of error squares method should help me with that because it will give less weight to pixels that are just part of some resulting blur and more weight to pixels that are noise that wasn't remove too well. Thanks for the input, though. It's an important thing to take into consideration. – shwartz Dec 25 '11 at 16:13

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The problem with the mean-square error metric is that it doesn't represent well the visual quality of the restored image. To address that, some other metrics have been developed. One that is quite popular now is called Structural Similarity. The source code for it can be found here.

nojka_kruva
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  • That's interesting. I've read a bit, without going into formula details since it seems a little too much for my case (nothing professional, just a test I'm doing on my assignment results). – shwartz Dec 25 '11 at 16:22
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My colleagues working on noise redution always use Signal To Noise Ratio (SNR) to compare the quality of the denoising: http://en.wikipedia.org/wiki/Signal-to-noise_ratio

Here are some scientific articles of my colleague Julien Mairal doing state-of-the-art noise reduction: http://www.di.ens.fr/~mairal/index.php

Oli
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  • I've seen a section there regarding SNR in images, calculated by mean to std. deviation ratio. I can't exactly see how that helps because I don't know how to measure the amount of noise in the denoised image (that's sort of what I'm trying to do). Anyway, I can see the resemblance of this SNR definition to the definition of Z-Score (AKA Standard score) and as I understand, it's a useful measure for comparing means taken from different populations, but in this case I'm using the same image for comparison of the method so that might be a bit of an overkill for my case. – shwartz Dec 25 '11 at 16:07
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The obvious distance to use is the sum of the squares of the pixel errors. The squared pixel error would be (p1 - p2)^2 for a grayscale image (the intensity of the two pixels are p1 and p2), or (r1 - r2)^2 + (g1 - g2)^2 + (b1 - b2)^2 if you have a RGB image (the colors of the two pixels are (r1, g1, b1) and (r2, g2, b2)). You can refine this a bit by scaling the RGB components differently to compensate for the fact that the human eye responds to blue less strongly than green and red.

  • Is this a common method for result comparison? Just by looking I can't say I like any of the results since the noise is not reduced enough for my taste, but that's probably as good as it can get using just convolution (which are my instructions). – shwartz Dec 24 '11 at 17:13
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    Yes, sum-of-squares error is commonly used in many fields. It's attractive due to its ease of computation and the fact that it directly represents the difference between "experiment" and "model" (terms used loosely here). – reve_etrange Dec 25 '11 at 01:55