From the video tutorial is seems relatively straightforward. I guess the basis selection is a fundamental issue that will be problem-specific.
I will have to try it with some concrete examples. The first question I have is, will it still work if you have a lot of high frequency noise? In the cases I'm thinking either there is measurement noise or just other jitter. So while the lower frequencies are sparse but I guess the higher frequencies not so much. I can't bandpass the data b/c it's got lots of holes or it's irregularly spaced.
Have fun on your discovery journey.