# Write up ZOGY / preconvolved A&L hybrid image subtraction algorithm

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#### Details

• Type: Story
• Status: In Review
• Resolution: Unresolved
• Fix Version/s: None
• Component/s:
• 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 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.

Basic idea:

• 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).

#### Activity

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Jim Bosch added a comment -

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!

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Jim Bosch added a comment - 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!
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Leanne Guy added a comment -

Jim will wrap up the first version of this TN and issue it. We will revisit the topic once in Operations

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Leanne Guy added a comment - Jim will wrap up the first version of this TN and issue it. We will revisit the topic once in Operations
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Jim Bosch added a comment -

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

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Jim Bosch added a comment - 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

#### People

Assignee:
Jim Bosch
Reporter:
Jim Bosch
Reviewers:
Bruno Sanchez
Watchers:
Bruno Sanchez, Jim Bosch, Leanne Guy