Wavelet Jumps

Mostly just a looming todo item for me so that I can feel ok about putting this on the back burner and work on more pressing things.

Finding jumps with a matched filter seems to mostly work but there are some issues namely:

1. A fourier space convolution doesn't really like the sharp discontinuity
2. Real space convolution are slow...

But wavelets make a lot of sense here since they are good at dealing with these sorts of localized features.

A naive attempt of looking at the CWT with a gaus1 wavelet seems to work well, but CWTs are probably more expensive than we need. This paper uses a DWT dydatic scales and seems to be the basis of a lot of modern approaches (though I cannot find a python implementation of the wavelet they use). This paper is a good followup with more information about dealing with noise.

Regardless of the exact technique used I think my takeaway is that using methods like this to then get an estimate of the Lipshitz regularity would be a very powerful technique in our flagging toolkit (since that also get us glitches at the same time but in a way where we know what is what). This paper is a good overview of estimating alpha.

I can imagine two modes here that we could use:

1. Estimate alpha at each point in the TOD and then use that to flag jumps and gltiches.
2. Do a cheap but perhaps false positive prone selection (ie: a thresh on the gradient, this can be done in the wavelett basis as well) and then estimate alpha in each of the flagged zones to kill false positives.

Overall I think that these sorts of wavelet techniques have the potential to be the final boss of giltch and jump flagging and merit a detailed look (the literature on this specific application seems deep). Will try to get something worthy of a PR cobbled together in the coming weeks.