Stoked by having finished my first first-author paper in a long while, I had a call with Daniel Foreman-Mackey in which I proposed to him that I try to finish a paper every week until I got through my backlog! He talked me down to one paper per month, and we agreed that our MCMC tutorial document should be next. He argued that we should add exercises (it is, after all, a chapter of the book I will never write). I agreed and wrote an exercise later in the day. I have a bunch more to go.
In the afternoon, I had a discussion with Leslie Greengard of my results on imaging molecules at random, unknown (yes, random=unknown) orientations with single-photon images. We discussed two big issues. The first is writing and testing analytic derivatives of my fully marginalized likelihood function (which is the objective function I (horror) optimize for this project). The other issue is representation for the molecule. We discussed many options and tentatively settled on a simple linear parameterization in real space (not Fourier space). Still confused; Greengard points out that it is confusing because there genuinely is no simple answer: There are no bases with elements that are compact in both Fourier space and real space, for deep, deep reasons.
Just curious, but what's the reason wavelets aren't appropriate? They can be compact in both real and frequency space, after all.
ReplyDelete- Simeon Bird
Compact in terms of, say, FWHM, but not compact in terms of *support*.
ReplyDelete...And I need compact in terms of support to (trivially) get sparseness.
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