And most of the image and video processing literature leads with what's

called additive noise. The noise is added to the image.

That's not what happens in all real cameras in all real acquisition devices,

for example. There is also multiplicative noise.

Very often, were basically all these, basically the degradation gets multiplied

by some noise. There are other types of noise that

happens, but these are some, two of the most common.

The most common of all is additive. Some literature, but much more limited,

addresses multiplicative noise. One of the effects of multiplicative

noise is that the amount of noise depends on the signal itself.

So, if the pixel value is three, we're multiplying three, but if the pixel value

is ten, we're multiplying ten, and then the amount of noise much, might be much

larger. And with additive noise, that doesn't

happen. So, it's basically kind of

image-independent denoise. Now, there is a way to transform

multiplicative noise into additive noise so we can enjoy all of the literature in

additive noise and also work kind of with a small trick applied also to

multiplicative noise. And I wonder if you know what trick can

we use to do that. Maybe think for a second before I give

you the answer. So, the question is very simple.

Think for yourself if you know what to do with multiplicative noise so you

transform it to additive noise. And let's think and I'll give you the

answer very soon, okay?

You just spend some time thinking. Maybe you go to the answer very fast.

Maybe you go to the answer after a while or maybe you are waiting for me to give

you the answer. And the idea is very simple.

If you have multiplicative noise instead of additive noise,

let me erase here, so I have everything to write down.

So, if you are multiplying two numbers, a times b, I can take the logarithmic of

those, of the product of those two numbers.

And that's equal to the logarithmic of a plus the log of b. So, I have trans, if b

was my noise, I basically transform it into additive noise.

So, instead of working with the image, I'm going to work with the logarithmic

version of the image and I'm going to work with the logarithmic component of

the noise. So basically, you give me the degradation

g, I take the log of g, and I treat everything that is now from

now on as it was additive noise. When I finish recovering it, I basically

have to invert this operation. And that's an exponential function.

So, that's one of the reasons that a lot of the literature has basically

concentrated on additive noise because of this trick.

Now, this trick has its own problems in particular because if you don't really

remove all the noise, the exponent can make it much, much larger.

But it's an important trick that basically makes our additive noise,

restoration techniques also applicable to multiplicative noise with some caveats

and some limitations. So, having now a concept of what is image

restoration, let's just talk in the next theory about

noise. What type of noise can we have in an

image? Where do they come from?

So, see you in the next video to deal with that topic.

Thank you.