Is there some "secret sauce" or special image processing that makes it possible to see these dim, diffuse areas above sensor noise?
Regardless of what type of camera one is using, the "secret" to getting good Milky Way images is to shoot from an area with virtually no light pollution at a time when the moon is below the horizon and the sun is at least 18° below the horizon. In other words, you want to have very dark skies. High altitude, low amounts of moisture or dust in the air, and cooler temperatures that result in less atmospheric turbulence also help.
The next requirement for a camera with limited light gathering capability is to gather enough light.
Since light gathering in astronomy has nothing to do with f-number and everything to do with absolute aperture (the actual diameter of the entrance pupil), cell phones are extremely limited at this point.
There are mainly two ways to gather more light in astrophotography.
- Mount the camera on a device, called a tracking mount, that counteracts the apparent motion of the sky so that long exposures may be used without getting 'star trails'.
- Take multiple shorter exposures and "stack" them using a post processing application made for combining multiple images. Each frame will need to be aligned with the others and the edges may be cropped to exclude parts of the sky that are not included in all of the frames.
Ideally, one can combine both methods.
In either case, the sky and the foreground will need to be captured separately. The first of your two examples shows some fairly obvious masking on the edges of the trees in the foreground.
With all of that out of the way, let's talk about the camera(s) in the Pixel 4.
No one knows anything for sure yet. The phone has not been officially released. It's quite possible that the phone is doing multiple exposures and combining the images to reduce the influence of Poisson distribution (shot) noise. It's possible that other computational photography is being applied. But all of that is purely speculative at this point.
There's also another method many folks use to get astro photos with camera phones:
- Use a bright, wide field telescope with a large aperture and set the camera at the proper distance from the eyepiece for the image to be in focus. There are accessories available that fit specific eyepieces to hold the camera in the correct position.