~]

So, yeah, welcome to multimedia security in 2018.

Last time we talked about photo response non-uniformity to identify a device.

And I would like to add a couple of details.

Okay.

First of all, I think I did not talk about a noise model for this PRNU application, right?

So that is something that is typically done very early on in the discussion,

but I sort of came from an application perspective, so let's add it now.

Let's call it image formation model.

And that essentially contains the noise.

So the assumption is that an observed pixel y consists of like the ideal signal

in terms of photons hitting the sensor x plus some source or some shot noise eta.

This is multiplied, I'd write something to this, by a multiplicative term f.

That's going to be our photo response non-uniformity.

And then we have two more sources of noise.

One is the dark current and one is, I think it was the readout noise, epsilon.

So let me explain all these symbols.

So y is the observed pixel intensity.

x is the ideal signal if we would have a perfect measurement device.

Eta denotes shot noise.

F is the PRNU.

C is dark current.

And this is electronic noise.

So the idea is that eta, C, and epsilon, they have different realizations from image to image.

That means if you hold the camera or if you statically mount the camera somewhere

and you twice press the trigger, take two pictures,

you will have different realizations of eta, C, and epsilon.

And that's actually the reason why the extraction of the fingerprint is proposed to be done by averaging a large number of pictures.

Because then eta, C, and epsilon average out and what we end up having is something like a product of f times x.

And then we perform the high-pass filtering in order to get as much of f as possible.

And if you have different image content, then x also averages out.

And we ideally just end up with the PRNU signal f.

That's the idea.

I mean, it never works like this.

But that's the whole idea.

So let's put this down.

So eta, C, and epsilon vary from...

No, that's not...

So let's say eta and epsilon vary from image to image.

And x and C vary with image content.

And f is fixed since maybe you remember it from before Christmas.

It's a property of the mask, like the illuminated area on the sensor.

Depending on how it comes out of the production line, the area is a little bit larger or a little bit smaller.

But this intuitively also makes clear this area does not change with changing environmental conditions.

So f is fixed since it is determined during manufacturing of the sensor.

So it's the photosensitive area.

Okay.

So this means if we average multiple images with little and varying content,

little, yet varying content, f and high pass...

Sorry, high pass filtering comes before.