> On its face it seems trivial

To me it seems completely impossible. How exactly do you expect to replace the missing information? Statistically from the neighboring pixels or frames? That works if your goal is to make an image prettier, but if you want to make measurements on the data "inventing" the background is not good enough.

Take many short expo images, and integrate them. This way you will have smaller streaks.

Yes, the sats will occlude things anyway, and their brightness is a big problem, but they are fast moving, they can be mitigated by moving to may short expo images combined. Yes, it's an undue burden, SpaceX should do more, but they can't solve it completely.

The readout time for astronomy CCDs is typically between 2 and 30s (going faster produces more noise), so there is a lower limit on how short you can make exposures.

In LEO the apparent movement of satellites is around 3.6 arcmin per second, which means for an average sized detector that covers maybe 20 arcmin it takes about 6s to produce a streak that covers the full length of the detector (bit longer depending on the angle). If you want it to cover less than 50% of the length of the detector you have to limit your exposure time to under 3s, which means your duty cycle will be between 60% (if you have a fast camera) and 10%(!).

And that's without even considering the loss of sensitivity you incur, because each image will have lower signal to noise since even with those long readout time the readout noise is still significant.

I'm not sure you're thinking about it the right way. Or maybe I'm not. It seems you're assuming that every exposure you take will have a streak in the same spot from a satellite. It's more realistic that a large portion of exposures will have no streak at all, or that if you re-exposed a detector on the same piece of sky, any streak it would see the second time would be in a different place than the first. So if you expose twice and do some basic interpolation to remove the streaks, you would end up with an equivalent zero-satellite image from two exposures.

What am I missing?

The piece that people are missing is the concept of SNR, or signal-to-noise ratio. These streaks are noise, which raises your noise floor and thus raises your detection threshold. Think of the way your eyes adjust to bright light - you can no longer see dim things around it even if they aren't obscured.

Ok, I understand, thanks for clarifying. My next question would be how many exposures would you need in a real-world setting to mitigate the issue? Ex. what's the actual likelihood of a satellite crossing your target piece of sky during a randomly chosen exposure, and how long will it be in the exposure, messing with your SNR?

First of all, as GP pointed out: whose cost?

Second of all: I highly doubt that this is "trivial", given that observatories are built in the most remote areas of the planet because light pollution was already an enormous problem before these satellites appeared, despite the extra costs that adds to any such project.

Light pollution is global, while a satellite streak is localised to a part of an image. These are not the same problem.

It's the other way around. It's possible to escape light pollution by moving away from electrified areas, whereas satellite streak ruins observations in every part of the world. Besides, the streaks are not really localized in the image. Its glow reportedly extends up to 15 arc seconds. That's a very large area for a carefully exposed array.

I meant light pollution affects the entire image, while a streak affects only part of it, which you can just remove.

A 30 arcsec stripe on an (apparently average) 20 arcmin detector is 2.5% of the total area, so it's not a very large area.

Overall, 20000 satellites at any given time cover 20kπ15acsec² of sky area, which is 0.0005% of total sky area, and over 1 second (assuming a satellite speed of 3.6 arcmin per second) it's 0.02424% of the sky, so roughly 1.45% of the surface area of a 1 minute exposure would have to be thrown out. This assumes that satellite streaks don't overlap, with overlap it would be less.

The problem is with the exposure. 1min exposures are common in astrophotography, but astronomers are complaining about the types that need night-long exposure - ones that try to study cosmology, stellar composition etc. Many observations (like SDSS) are also large field observations that observe many objects simultaneously. Even a single streak can ruin an entire exposure. The odds just grow considerably.

In digital photography, an exposure of N seconds can be produced from the sum of N/K shorter exposures at K seconds. This is more of a nuisance than a devastating blow.