detect the stars during the day

The daytime sky (the blue sky) is bright but transparent. That means that the stars are visible during the day. Very good visual astronomers I know have once or twice pointed out Venus to me during the day. I'm not so good as that!

I think it would be an interesting and valuable project for astronomy education, and maybe also image processing, to do the following: Take a large number of digital-camera images of the blue sky during some short period of one sunny day. Take these images and post-process them to detect the stars. That is, make an image of what you would have seen if the Sun had gone dark.

There was a time in my life that I thought this project was easy. I have made some superficial attempts and I no longer think that. One idea I have (but haven't pursued) is to do this on a day that the Moon is visible, and use the Moon as a stacking reference. It isn't a perfect reference (it's a wandering star) but it's probably good enough for a first guess at alignment. Because something about this project depends on the ratio of intensity (sky brightness) to flux (star brightness), which have different units (!), I think this project must be easier to do with a telephoto lens.

compare EM to other optimization algorithms

For many problems, the computer scientists tell us to use expectation maximization. For example, in fitting a distribution with a mixture of Gaussians, EM is the bee's knees, apparently. This surprises me, because the EM optimization is so slow and predictable; I am guessing that a more aggressive optimization might beat it. Of course a more aggressive optimization might not be protected by the same guarantees as EM (which is super stable, even in high dimensions). It would be a service to humanity to investigate this and report places where EM can be beat. Of course this may all have been done; I would ask my local experts before embarking.