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).
DECaLS and HST
Image credit: Dark Energy Camera Legacy Survey / NASA / ESA / Hubble / Huang et al.
In practice
MuSCADeT/SCARLET
F435w: \(I_2\)
F606w: \(I_1\)
F814w: \(I_0\)
$$I_j = H_j \sum_i a_{j,i}m_i + N_j$$
$$m_0$$
$$m_1$$
$$I$$
SCARLET
Melchior et al. 2016 ( arXiv:1802.10157)
Linear Optimisation
Constraints: Positivity, Monotonicity, Bounding.
Functional decompositions:
The Starlet transfrom
Starlet coefficients
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
Reconstruction: known model for the mass
Reconstruction : wrong mass model (unknown substructure)
Strong gravitational lens searches
Automated searches rely heavily on ML to find strong lens candidates.
Pixel-level joint processing takes the best of both worlds:
Expectations:
pixels
wavelength
pixels
pixels
HST cosmos, F814w
HSC DR2, grizy
\(Y_1\):
\(Y_2\):
pixels
Joint reconstruction
How to achieve these goals:
Better models and better constraints
Lensing :
Multi-resolution deblending:
Multi-resolution lensing:
Joint inference from images at different resolutions
How to achieve these goals:
Better models and better constraints
Tools from machine learning
Credit: Morningstar et al. 2019
To conclude
Modelling astro images for
Deblending
Galaxy light profile
Telescope refraction (convolution)
Instrument acquisition (pixelation)
Instrumental noise
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)
$$I_j = R*P_j * \sum_i a_{j,i}\Phi s_i + N_j, \qquad m_i = \Phi s_i$$
The algorithm
Colours are extracted from the scene using Principal Component Analysis (PCA) of the multi-band pixels
SCARLET
$$I_j = R*P_j * \sum_{i,n} a_{j,i,n}m_{i,n} +N_j$$
Melchior et al. 2016 ( arXiv:1802.10157)
Functional decompositions:
The Starlet transfrom
Illustration: Detection in crowded fields
Credit: Fred Moolekamp
NGC 6569
Sep detection
NGC 6569
Starlet+Sep detection
NGC 6569
Starlet level 1
$$I_j = R*P_j * \sum_{i,n} a_{j,i,n}m_{i,n}$$
In scarlet
$$p(m) = \prod_k p(m_k|m_{k-1}, ..., s_0) $$
\( \tilde{M} = \underset{M}{argmin}\) \( \frac{1}{2}||I-HAM||^2_2 \) \(+\) \(\sum_i p(m_i)\)