1. (and especially Robert Lupton and Dustin Lang)
Deblending
Jim Bosch
for Data Management
(and especially Robert Lupton and Dustin Lang)

2. There Will Be Blends LSST will go deep: LSST is on the ground:
We’ll detect fainter objects.
We’ll see the low surface brightness wings of everything.
LSST is on the ground:
Even under the best conditions, image quality won’t be as good as what we’d get from space

3. There Will Be Blends
From David Kirkby (in prep)

4. Kinds of Blends

5. Space and Ground
HST WFC3 F125
Subaru HSC i

6. Case 1: Unknown Unknowns
If sources are so close we can’t tell they’re blended, there’s nothing the DM pipelines can do.
Data from space could help, but using this will likely be Level 3.
Mostly, we’ll have to deal with these statistically in the science analysis.

7. Space and Ground
HST WFC3 F125
Subaru HSC i

8. Case 2: Known Unknowns
We believe there may be more than one source in a particular region.
We want to measure the properties of the sources in as if they were isolated.
Simultaneous model-fitting is one option, but it may not be the best one.
Some popular measurements (e.g. aperture fluxes, image moments) require that we actually try to split up the pixels.
We don’t have good models for some kinds of sources (e.g. galaxies).

9. Deblending Stars
This is easy, if we have a good PSF model: just fit models simultaneously.
Because stars (at any given epoch) are completely represented by positions and fluxes, there’s no need to do additional measurements.
If we don’t have enough isolated stars to build a PSF model, we need a crowded field code.

10. Deblending Galaxies
Unlike stars, we don’t have good models for galaxies.
This is clearly bad new for bright, well-resolved galaxies.
It might also be bad news for faint or poorly-resolved galaxies.

11. The SDSS Deblender: a Starting point

12. The SDSS Deblender: Detection
In each band, we smooth the image, then detect above-threshold regions (Footprints). We then grow these regions by the size of the smoothing kernel.
Within each Footprint, we find one or more Peaks.
SDSS

13. The SDSS Deblender: Merging/Culling
We compute the spatial union of all the Footprints from different bands, epochs, smoothing kernels.
Within each Footprint, we merge all the Peaks from the different detection images, culling those that appear to represent the same source.

14. The SDSS Deblender: Symmetric Templates
true source profiles
pixel values 𝑧
templates 𝑇
For each Peak 𝑖 and pixel 𝑥, create a template 𝑇 𝑖,𝑥 that is the minimum of the pixel value 𝑧 𝑥 and its reflection about the peak 𝑧 ~𝑥 . Do a linear fit for the amplitudes 𝛼 𝑖 of all templates by minimizing: 𝑥 𝑧 𝑥 − 𝑖 𝛼 𝑖 𝑇 𝑖,𝑥 2 Compute deblended pixel values: 𝑧 𝑥,𝑖 ∗ = 𝛼 𝑖 𝑇 𝑖,𝑥 𝑧 𝑥 𝑗 𝛼 𝑗 𝑇 𝑗,𝑥
residuals
deblended pixels 𝑧 ∗

15. The SDSS Deblender: Symmetric Templates
𝒛 𝒙
𝒛 ~𝒙
SDSS

16. The SDSS Deblender: Heuristics
If the dot product of any two templates is close to one, drop one of them.
If a template looks a lot like the PSF model, use the PSF model as the template instead.
Put limits on how sharp a template’s features can be.

17. The SDSS Deblender: Measurement
We call the outputs of the deblender HeavyFootprints: they’re Footprints that also hold the pixels of the deblended children.
When we measure a source, we replace every other source’s Footprint with noise first.
In addition to measuring the child sources, we also measure the parents (because we might have been wrong about it being a blend, or the deblender may have done more harm than good).

18. Features of the SDSS Deblender
We can run any measurement algorithm we can run on isolated sources.
Flux is conserved as it is split up.
No simple assumptions about galaxy morphology: not only is 180˚ rotation a weak constraint, it’s only enforced on the templates, not the deblended pixels.

19. Weaknesses of the SDSS Deblender
Only Peaks are shared between bands; no good way to generate reasonable templates for drop-out sources.
No way to account for multiple epochs with different PSF.
Doesn’t handle uncertainty rigorously.
Vetted on a survey with a much less severe blending problem.

20. What next?

21. Detection for LSST Detection will happen on multiple coadds:
different bands (or weighted combinations of bands)
different smoothings (i.e. morphological filters)
...and difference images.
We need to merge these detections in order to deblend consistently.
We need to transfer the deblender outputs back to images with different bands, PSFs, WCSs, and observation dates.

22. Going Multi-Epoch
We can convolve templates derived in one band or image with a difference kernel to generate one appropriate for a different band or image.
We can use point-source templates for drop-outs.
We can use PSF-convolved analytic models as templates.

23. ...or Simultaneous Fitting?
We’re going to use simple galaxy models for many of our most important measurements; do we gain anything (or lose anything!) by redistributing pixel flux using a more flexible model first?
Can we make galaxy models flexible enough to make model biases unimportant?
Flux redistribution with templates may still be useful as a starting point – it’s a lot faster than a high-dimensional nonlinear fit.

24. More on Galaxy Modeling
What should we let vary between bands?
How flexible should models be?
If they’re very flexible, how do we handle low SNR sources?
Can we afford to sample rather than fit?
If we need priors, where do they come from?
Do we fit a star model and a galaxy model to everything?
Come to the breakout session at 1:30pm today!

25. Using Colors?
There’s a lot more information in the spectral dimension that could be used in deblending.
We don’t want to bias downstream algorithms (e.g. photo-zs) or make it less likely to find new and interesting objects that don’t have “normal” colors.

26. SDSS functionality visit images simultaneous fitting final models
coaddition
image subtraction
preliminary models
coadd
images
replace neighbors with noise, measure
difference
images
detect
SDSS functionality
detect
Footprints & Peaks
generate templates, reapportion pixel fluxes
Footprints & Peaks
merge/cull
coadd Heavy Footprints
Footprints & Peaks

27. The LSST Prototype Deblender
The LSST DM Stack includes a limited reimplementation of the SDSS Deblender.
We don’t have any code for the peak merge/cull stage, so we can’t deblend across multiple bands in a consistent way.
We don’t have some of the heuristics that were used in SDSS.

28. What We Don’t Know Can Hurt Us
The presence of a LRG affects the measurement of the properties of sources arcminutes away.
This is because undetected galaxies cluster with the galaxies we do detect, and that upsets the measurement algorithms in a systematic way.
Error in measurements of simulated galaxies injected into real data.
Huff and Graves (2014)