video magnification on eta Carinae

We should apply the video magnification methods of Bill Freeman (MIT) to the spectacular HST images of expanding star eta Carinae. The motion in the HST images is a bit subtle, but it sure wouldn't be if we fired up the Freeman tricks. One of the cleverest of his tricks is to take the Fourier Transform of each image and then magnify the phase differences. This ensures that the thing being magnified is global and smooth, in some sense. The one respect in which Freeman's methods would have to be generalized is that the data are not from a single, video source: The different images were taken through different filters on different cameras and with different exposure times.

extract low-resolution spectra from diffraction spikes

In imaging from a telescope with a secondary on a spider (for example, in HST imaging), bright stars show diffraction spikes. More generally, the outer parts of the point-spread function are related to the Fourier Transform of the small-scale features in the entrance aperture. The scale at which this Fourier Transform imprints on the focal plane is linearly related to wavelength (just as the angular size of the diffraction-limited PSF goes as wavelength over aperture).

This means that the diffraction spikes coming from stars contain low-resolution spectra of those stars! That is, you ought to be able to extract spectral information from the spikes. It won't be good, but it should permit measurements of colors or temperatures or SED slopes with even single-band imaging, and aid in star–quasar classification. Indeed, in HST press-release images, you can see that the diffraction spikes are little "rainbows" (see below).

The project is to take wide-band imaging from HST, in fields where stars have been measured either in multiple bands or else spectroscopically, and show that some of the scientific results could have been extracted from the single, wide band directly using the diffraction features.

cosmic-ray identification

Take a set of HST data from one filter and exposure time (to start; later we will generalize) that have been CR-split (meaning: two images at each pointing). Shift-and-difference these split images to confidently identify a large number of cosmic rays. Pull out 5x5 image patches centered on cosmic-ray-corrupted pixels and 5x5 image patches not centered on cosmic-ray-corrupted pixels. Use these labeled data as training data for a supervised method that finds cosmic rays in single-image (not-CR-split) data. Improve value of HST data for all and obtain enormous financial gift from NASA in thanks (well, not really).

Notes: The most informative pixel patches will be those with faint cosmic ray pixels and those with bright stars that mimic cosmic rays. Some of this work has been started with (now graduated) NYU undergraduate Andrew Flockhart.