Section 1- What is Gaussian Noise

So last time we talked about, adding a noise function to an image function, so here (Figure 1)

                                                                          Figure 1. Gaussian Noise 

we have our noise, defined as just this random thing scaled by the sigma, our output was just the image plus the noise. And we said, remember, you have to worry about the size of the sigma in respect to the range of the image, so if your image is 0 to 255, a sigma five might be plausible, if your image goes 0 to 1, size of sigma five is not plausible, so you have worry about how those come together.

Section 2- How to remove Noise from image 

Now, suppose there was noise in your image, and you wanted to remove the noise, how might you think about doing that? Now I'm sure, bunch of you have suggestions that are kind of similar. Here, here's the typical one, right? Let me replace the value of each pixel, with sort of an average of the pixels around it. Okay? So. Let's think about what that would look like in 1D, and then we'll go to 2D, and we'll talk about why is this the right thing to do or when is this not the right thing to do, all right. So, here's our first attempt, so, we're going to replace each pixel with an average of the values of the pixels neighborhood, and this is referred to as a moving average, so here I have some location here, and I just take the average value and I put it down there, okay? And then I would move my little, what's called window as I take my average, and I get a new value, and I get another one, and then eventually, I would get this new somewhat smoothed version of the original, and it's smoothed meaning that we sort of averaged of the things locally.