MADNESS
Maximum-A-posteriori solution with Deep generative NEtworks
for Source Separation
Biswajit Biswas, Eric Aubourg, Alexandre Boucaud, Axel Guinot, Junpeng Lao, Cécile Roucelle
BDL Workshop
23rd June, 2022
Surveys and Challenges
Large survey of Space and Time (LSST) at Vera Rubin Observatory:
more depth + area of coverage ⇒ More statistics!
greater depth means more complex data!
~ Galaxies (60% in LSST ) are expected to overlap (blending) in images due to increased depth
HSC ultradeep image
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ML for Deblending
Arcelin et al (arXiv:2005.12039)
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Denoising (Single source)
Where, 𝑥* is the maximum a posteriori probability (MAP) estimate
Input image (𝚢)
Predicted image (𝑥)
Residual (𝚢-𝑥)
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Train VAE as generative model
𝑥
𝑥
For example: Lanusse et al (arXiv:2008.03833)
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Training:
Regularization term
Reconstruction term
MAP estimate in latent space
Where, 𝑧* is the maximum a posteriori probability estimate in the latent space
Going to the latent space
Predicted galaxy ( x )
Input image ( 𝚢 )
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How to choose a prior?
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Normalizing flow
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Minimization
Predicted galaxy ( x )
Input image ( 𝚢 )
Where, 𝑧* is the maximum a posteriori probability estimate in the latent space
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Deblending (Multiple sources)
Reconstructed field
Probability that predictions are galaxies!
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Deblending Example
Input image
Predictions
Residual image
(input - predictions)
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Moving to a larger field…
Input field (501 x 501)
Sinh-1 ( Input field )
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Input field
predicted field
residual field
(Input - predicted)
Moving to a larger field…
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Preliminary results*
Compare with SOTA
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Conclusion and Future work
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Thank you!