Yes, it's a many-to-one. Ignoring optical aberrations and losses from the lens, there's always additive noise that does not depend on the number of photons inc

Yes, it's a many-to-one. Ignoring optical aberrations and losses from the lens, there's always additive noise that does not depend on the number of photons incident on the sensor. That could be dark/thermal noise, noise in the readout electronics, noise coupled in from external RF sources, etc. You could expose the detector with exactly the same number of photons 1000 times and get 1000 different images.