Multi-Band and Multi-Resolution Deblending: Why it is Important to Leverage All Available Information

Fred Moolekamp

How big is the problem?

Relationship Between Blending and Detection

Exercise 1a

• Mark all peaks in this image
• For each peak, circle it’s approximate footprint

*LSST-g

*Simulated images made with galsim

Exercise 1b

• Mark all peaks in this image
• For each peak, circle it’s approximate footprint

LSST-i

Exercise 1c

• Mark all peaks in this image
• For each peak, circle it’s approximate footprint

LSST-gri

Exercise 1d

• Mark all peaks in this image
• For each peak, circle it’s approximate footprint

HST

High resolution color

HST-color

Low-Resolution Solution

LSST-color

This is true for real data as well

HSC-i

HSC-riz

HST

Effects of Blending on Measurements

Question 1

How will the neighbor affect the center of flux measurement? Does it depend on how the center of flux is estimated? If so, how? If not, why not?

Answer 1

• The center of flux will be shifted toward the neighboring object.
• The amount of shift will vary between centering techniques but will always be qualitatively the same.

Exercise 2

1. What properties of the neighboring object will affect the shift in the center of flux of its neighbor?
2. Think of some ways that some/all of these properties can be used to tell us something about the blend

Solution 2 (what I came up with)

1. Here’s what I came up with:
1. Distance between centers
2. Relative brightness
3. Size of the object
4. Colors (brightness will differ by wavelength)
5. Ellipticity
6. orientation
2. If the sources differ in color, the center of flux in each band will have different shifts.
• This can give us some information about the difference in SEDs of the two objects.
• Conversely, if we know the SEDs this tells us something about how much the sources are blended

Question 2

• How will the neighbor affect the shape measurement (2nd moment)?

Answer 2

• This depends on both the orientation of both sources (parallel vs perpendicular to one another) and the direction of the line connecting their centers
• If the sources are parallel and oriented in the same direction as their centers the shapes will be more elliptical
• If the sources are parallel and oriented perpendicular to their centers they will be less elliptical
• If the sources are perpendicular to one another then they will be less elliptical, regardless of the direction between their centers

More elliptical

Less elliptical

Building a Deblender

A note about color mapping

• Most of the images use a modified version of the color mapping scheme of Lupton et al. 2004

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• So keep in mind that the faint features around the outskirts of sources are very faint compared to the flux toward the center

Examples

Linear

Asinh

Sample of Galaxies from a single HSC field

Sample of Galaxies from a single HSC field

Sample of Galaxies from a single HSC field

Sample of Galaxies from a single HSC field

Sample of Galaxies from a single HSC field

Exercise 3

What other information might we be able to leverage while deblending?

Solution 3

Here’s some that I came up with:

• Single component SED’s
• Symmetry
• Monotonicity
• Spectral information

Single Component SED’s

• Most astrophysical sources can be modelled as a collection of components, each with an SED that is nearly constant over its morphology
• This decomposition is a key feature of our ability to deconstruct sources in a blend

Monotonicity

• Most observable astrophysical features are centrally located
• More complicated structures, like grand design spirals, can be modelled as a collection of monotonic components (different stellar/gaseous populations)

Monotonicity

Without monotonicity:

Monotonicity

With monotonicity but no symmetry

Flux lost to neighbor

Flux stolen from neighbor

Symmetry

• Less stringent than parametric models (Sersic radial profile with an ellipticity)
• Most galaxies are surprisingly symmetric

Examples

Examples

Symmetry

• Adding 180^○ symmetry allows us to separate flux between the sources

Exercise 4

• What types of blends will be the most challenging for this type of deblender?

Problems:

• The large galaxy is irregular (not symmetric or monotonic)

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• Most of the sources blended with it are undetected

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At a minimum we need to improve our detection algorithms to do better on blends like this. Any undetected sources are catastrophic to the deblender.

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• Somya Kamath is working on a mask-R CNN approach to finding undetected sources in scarlet residuals

Data

Model

Problem: only 4 components detected for the central galaxy

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To solve we need to have an intelligent way to determine when to model a source with multiple components, and a clever way to initialize them.

Data

Model

Problems:

• 3 galaxies in a row make it tough to model the central object
• The bright grand design spiral is not symmetric and has multiple components

Question 3

What is the configuration of this blend?

Question 4

• Both models to the right used scarlet with different constraints.
• Which result is better?

Evaluating Results

Residuals do not tell the whole story

Total residual: 312

Total residual: 399

Question 5: Discussion

What metrics should we use to determine that the deblender is doing a good job when there is no ground truth?

What I’d like you to take away from this lesson

• Deblending is impossible hard!
• Simultaneous processing of multiple images (in color, seeing, and resolution) is key to improving results for both detection and deblending
• Minimal priors are needed to generate feasible results
• No matter what debleding solution LSST chooses, we need to be careful about how we interpret the results and measure the biases

Resources for more information:

• scarlet paper
• scarlet docs
• BTF presentations on scarlet: PartI, Part II, Part III, Part IV
• BTF presentation on Metacal comparisons of scarlet and MOF
• Sowmya Kamath’s presentations on detecting sources in scarlet residuals: Part I, Part II

Extras

Basic Model

Data

Model

Source 0

Source 1

Source 2

Source 3

Image from HSC Deep Field

Most constraints use proximal operators

Non-negativity:

Normalization:

Symmetry:

Monotonicity:

• Not a true proximal operator but a projection onto one representation of a monotonically decreasing solution