Multi-band Deblending with scarlet Fred Moolekamp Princeton - - PowerPoint PPT Presentation

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

1

Multi-band Deblending with scarlet
 
 Fred Moolekamp
 Princeton University
 
 LSST 2018 Blending Workshop
 August 14, 2018

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

2

The problem

• Blended scene:

Image from HSC COSMOS dataset (courtesy Peter Melchior)

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

3

The problem

• Use colors!

Image from HSC COSMOS dataset (courtesy Peter Melchior)

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

4

scarlet: Basic Model

Data Model Peak 0 Peak 1 Peak 2 Peak 3 Peak 4

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

5

scarlet: Basic Model

Model for a blend: We want to minimize: Use gradient decent and proximal operators to solve

M =

K

∑

k=1

Ak × Sk

f(A, S) = 1 2 ||Y − AS||2

2 + K

∑

i=1

(gA

i (Ai) + gS i (Si))

model

Data

non-smooth constraints

A S

components

bands

pixels

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

6

Initialization

1 5 10 27

• Build a symmetric, monotonic template

at each peak

• Use the monotonic templates to

calculate the average SED

Model at different iterations

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

7

Constraints

• SED Constraints
• Non-negative
• Sum to unity

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

8

Constraints

• Morphology Constraints:
• Non-negative
• L0 sparsity
• Soft symmetry:
• Monotonicity:
• Each pixel must be less than or equal to the sum
• f its reference pixels
• Only approximate constraint

Sk,n = (1 − σ) Sk,n−1 + σ 2 (Sk,n−1 + S†

k,n−1)

Peak Pixel Ref

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

9

180 degree Symmetry

• separates most objects

?

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

10

Monotonicity

• Forces flux to be non-

increasing radially from the peak

• Implemented as a

projection operator

• nto the space of

decreasing radial flux

?

10

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

11

PSF Deconvolution and Re-centering

• PSF convolution and fractional pixel shifts use linear

approximations

• Makes the model more complicated by solvable

Mb

k = Ab kTkiPb iiSik

k = source # i = pixel # b = band Data Model Fully De-Convolved Model

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

12

Problems with Full PSF De-Convolution

• The constraints act on the deconvolved space

(must be well sampled)

• Full deconvolution = morphology under sampled
• Results in artifacts in the models, for example:

deblended galaxy

Artifacts due to blending

Truth No PSF Full PSF Partial PSF

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

13

PSF Matching

• Target PSF is a moffat
• Create a difference kernel

in each babd to match the moffat

• The morphology in each

band is convolved with the difference kernel

LSST Project and Community Workshop 2018 • Tucson • August 13 - 17

#lsst2018

14

Conclusion

• The last stack can now run scarlet using the

MultibandDeblendTask and DeblendCoaddSourcesTask

• scarlet can also be run as a stand alone package
• See the documentation at http://scarlet.readthedocs.io
• Tutorials will be shown at the “Hands on Deblending”

workshop this afternoon

• See the scarlet paper at https://arxiv.org/abs/1802.10157
• download scarlet at https://github.com/fred3m/scarlet