Rémy Joseph
MLxCosmo December 17th 2020
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).
Modelling astro images for
Deblending
Galaxy light profile
Telescope refraction (convolution)
Instrument acquisition (pixelation)
Instrumental noise
In practice
Pixelated model
Robert Lupton
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)
SCARLET:
Modelling multi-band images
F435w
F606w
F814w
NASA/ESA: Hubble Frontier Fields, MACSJ 1149, Lotz et al. (2016)
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
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)
$$I_j = R*P_j * \sum_i a_{j,i}\Phi s_i + N_j, \qquad m_i = \Phi s_i$$
NASA/ESA: Hubble Frontier Fields, MACSJ 0416, Lotz et al. (2016)
Complex galaxies
F814w
F435w
RGB
MuSCADeT Red
MuSCADeT Blue
Low Surface Brightness Galaxies
On going work with Johnny Greco, Jiaxuan Li & Jenny Greene
HSC image
image-model
LSB model
Residuals
Reconstruction of strongly lensed source
Reconstruction of strongly lensed source
$$I_j = R*P_j * \sum_{i,n} a_{j,i,n}m_{i,n}$$
In scarlet
$$p(m) = \prod_k p(m_k|m_{k-1}, ..., s_0) $$
\( \tilde{M} = \underset{M}{argmin}\) \( \frac{1}{2}||I-HAM||^2_2 \) \(+\) \(\sum_i p(m_i)\)
Last thoughts
The algorithm
Colours are extracted from the scene using Principal Component Analysis (PCA) of the multi-band pixels
SCARLET
Melchior et al. 2016 ( arXiv:1802.10157)
Weakness (of the model): Monotonicity can causes trails and shadows.
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