Details

Type: Story

Status: In Review

Resolution: Unresolved

Fix Version/s: None

Component/s: DM Subsystem Science

Labels:None

Story Points:4

Team:DM Science

Urgent?:No
Description
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 dividebyzeros or dividebynoise yet. On this ticket, write it up more carefully and work through some 1d toy examples, producing a DMTN.
Basic idea:
 start with the ZOGY decorrelated "proper image subtraction" formula;
 replace all PSFs in the denominator by slightly narrower analytic (Gaussian or doubleGaussian) 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 GaussHermite bases are so useful there).
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!