I am well underway, now, with the first exercise/assignment. The goal is to create an image editor that lets you work on either the image or the Fourier transform of the image. I have only tested it under Safari and Firefox so far. I do intend to add excanvas into it later and test it on some other browsers.
If you are interested (and have Safari or Firefox), here is the current state.
Edit (four hours later): I have now debugged it under Firefox 3.5.2.
These are the original image, the Fourier transform in which I painted some green dots and phase-rotated the lowest-order frequencies, and the image after the inverse transform.