Flexible Image modelling for deblending and strong gravitational lensing

Rémy Joseph

Stockholm, Oct. 15 2021

Collaborators: Peter Melchior, Fred Moolekamp, Frederic Courbin (EPFL, SW), Jean-Luc Starck (CEA, FR), Aymeric Galan (EPFL), Austin Peel, Martin Millon (EPFL), François Lanusse (CNRS, FR), Jiaxuan Li (PKU), Jenny Greene, Johnny Greco (OSU).

MuSCADeT/SCARLET

• Colour-based: each band is a linear combination of monochromatic components

F435w: \(I_2\)

F606w: \(I_1\)

F814w: \(I_0\)

$$I_j = H_j \sum_i a_{j,i}m_i + N_j$$

$$m_0$$

$$m_1$$

$$I$$

Functional decompositions:

The Starlet transfrom

Starlet coefficients

• Multiscale transformation
• Decomposition in B-splines at different spatial scales

Starlet basis set

Low Surface Brightness Galaxies

On going work with Jiaxuan Li, Johnny Greco & Jenny Greene

HSC image

image-model

LSB model

Residuals

Reconstruction of strongly lensed source

Credit: Aymeric Galan

SLITronomy

Joseph et al. 2018

Galan et al. 2020

Strong gravitational lens searches

Automated searches rely heavily on ML to find strong lens candidates.

• ML finders are only as good as their training. e.g. Rojas et al. injects strongly lensed features in DES images to build a training set.
• ML finders identify ~1000s of candidates.
• Deblending for lens finding to help the finders (humans or not)

Modelling astro images for

Deblending

Constraints on starlet coefficients

Is achieved by reconstructing sparse fields in starlets:

\( \tilde{S} = \underset{S}{argmin}\) \( \frac{1}{2}||I-HA\Phi S||^2_2 \) \(+\) \(\lambda||S||_1\) \(+\) \(\mathcal{i}_+(\Phi S) \)

Likelihood           Sparsity      Positivity

                   (smoothness constraint)

MuSCADeT: Joseph et al. 2016 (arxiv:1603.00473)

GitHub: https://github.com/herjy/MuSCADeT

$$I_j = R*P_j * \sum_i a_{j,i}\Phi s_i + N_j, \qquad m_i = \Phi s_i$$

Functional decompositions:

The Starlet transfrom

Illustration: Detection in crowded fields

Credit: Fred Moolekamp

NGC 6569

Sep detection

$$I_j = R*P_j * \sum_{i,n} a_{j,i,n}m_{i,n}$$

PixelCNN as a prox

In scarlet

• Scarlet is flexible to the kind of constraints we can impose on morphology. We are now implementing priors PixelCNN Lanusse et al. 2019:

$$p(m) = \prod_k p(m_k|m_{k-1}, ..., s_0) $$

\( \tilde{M} = \underset{M}{argmin}\) \( \frac{1}{2}||I-HAM||^2_2 \) \(+\) \(\sum_i p(m_i)\)