Status: In Review
Fix Version/s: None
Component/s: DM Subsystem Science
I've had the question of how to combine ZOGY and A&L preconvolution more rigorously rumbling around in my head a while. I've just done some quick and dirty math to work it out and I haven't spotted any divide-by-zeros or divide-by-noise yet. On this ticket, write it up more carefully and work through some 1-d toy examples, producing a DMTN.
- start with the ZOGY decorrelated "proper image subtraction" formula;
- replace all PSFs in the denominator by slightly narrower analytic (Gaussian or double-Gaussian) approximations to avoid dividing by noise or zero (at the expense of not fully decorrelating);
- multiply both the numerator and the denominator by the (Fourier) ratio of the template PSF approximation to the true template PSF;
- gather terms to get the (known) preconvolution kernel on one end of the subtraction and the (unknown) difference kernel to solve for on the other end, with the subtraction yielding an residual image with approximately decorrelated noise, so you can easily do least squares.
I think this is going to be pretty good at avoiding net deconvolutions, but I think it might involve a difference kernel that isn't well sampled and hence is hard to work with in the image domain (but that's also true of A&L, in general, and perhaps a hint at why Gauss-Hermite bases are so useful there).
Jim will wrap up the first version of this TN and issue it. We will revisit the topic once in Operations
Thanks in advance for the review!
PR is here: https://github.com/lsst-dm/dmtn-196/pull/2
and rendered HTML is here: https://dmtn-196.lsst.io/v/DM-30808/index.html
Just skimmed DMTNs 21 and 179; the latter in particular gets really close to this idea but (I think) doesn't quite consider it. But I think it's entirely conceivable that when I work through this more carefully I'll encounter a good reason it wasn't considered (and either isn't viable or has some substantial challenges to overcome). We'll see!