Expression for speckle noise addition might need correction

[neeraj3029]

Description

The expression for speckled image is out = img + img * noise which translates to out = img * (noise+ 1) where noise is with given mean and variance. Speckle is a multiplicative noise, in my opinion should just be out = img * noise

[mkcor]

@neeraj3029 could you please share some references (textbooks and/or papers)? We may want to point to them even in the docs... Maybe it's just 'well-known' but, personally, my memories from grad school are not fresh at all, so I'd be happy to check out a good reference on the topic. :)

[neeraj3029]

Sure @mkcor! I got to know about it while working on the following papers from IEEE.

1. SAR Image Despeckling Using a Convolutional
   Neural Network (arXiv) (IEEE) - Equation (1) and the paragraph above

2. A Practical Approach for SAR Image Despeckling Using Deep Learning - Equation (1)

I could not find much implementations of multiplicative noise over the web, so I am not sure if the change I suggest is absolutely correct or not. However, after going through to the papers I thought I should point this out.

[mkcor]

Dear @neeraj3029,

Thank you for looking this up. I checked and the implementation is correct. Indeed, noise in out = img * (noise + 1) is speckle noise of zero mean:

scikit-image/skimage/util/noise.py

Lines 39 to 41 in a69d492

	mean : float, optional
	Mean of random distribution. Used in 'gaussian' and 'speckle'.
	Default : 0.

When the formula is expressed as Y = FX where X is the noise-free image and Y the noisy image, F is speckle noise of unit mean (so it's the same as a zero-mean speckle noise + 1).

References:

• https://arxiv.org/pdf/0912.1845.pdf
• https://medium.com/@sunil7545/speckle-vs-gaussian-noise-7f4f47230d82