Use of a Bayesian Approach for Generating Statistically Representative Sky Signals
Apply advanced Bayesian techniques to synthesize statistically representative sky signals. This project focuses on implementing Gibbs sampling for astrophysical data, offering a rigorous approach to overcoming optimization challenges in modern cosmological analysis.
This project is focused on enhancing our understanding of astronomical phenomena through the analysis of sky signals. It has been demonstrated that statistical component separation can significantly improve our understanding of the sky (e.g., [1]). We currently use a method based on scattering covariance statistics [2], developed from theoretical analyses of the way Convolutional Neural Networks (CNNs) operate. These statistics are highly effective in compressing information into lower dimensions. It has been shown that the synthesized structures inherit hidden physical properties of celestial bodies. A key advantage compared to neural networks is that this method does not require a large training dataset; in some cases, a single image is sufficient. The concept of this approach is to synthesize data that shares the same statistical properties as the observed sky data. In order to separate the signal of interest from the foregrounds (closer, non-cosmic signals such as emissions from our own galaxy) and noise (random, non-astronomical signals), the statistical information is first debiased. Unfortunately, this method relies on a gradient descent optimization to find a synthesized map with the desired statistical properties. This step is computationally intensive and may get stuck in local minima. Our aim is to employ a different paradigm to synthesize the target statistics based on a Bayesian approach, specifically using Gibbs sampling. In line with recent research on scattering transforms on the sphere, we will explore this method as a basis for new statistical component separation algorithms. Furthermore, the Bayesian approach will generate an ensemble of possible signals of interest that satisfy the statistical constraints, which is preferable to a single solution that might represent a local minimum.
Goal
The goal of this project is to test the Bayesian approach based on the Gibbs sampling paradigm using the dataset from previous research. Python software and data used by [1] are available, so the student will primarily focus on converting the optimization method in a Gibbs Sampler.
Learning outcome
- Learn to program a Bayesian approach (Gibbs Sampling).
- Learn to design an algorithm for state-of-the-art astrophysical data (galactic microwave emission from the Planck satellite) key information for modern observational cosmology.
Qualifications
- Strong mathematical background to facilitate understanding of the Bayesian approach.
- Proficiency in Python would be helpful. Experience with TensorFlow would be highly beneficial.
Supervisors
- Anne Fouilloux
Collaboration partners
This project will be carried out in collaboration with:
- Co-supervisor: Mathew Galloway, the Oslo Institute of Theoretical Astrophysics
- Co-supervisor: Jean-Marc Delouis, the Brest Laboratoire d’Océanographie Physique et Spatiale (France)
References
- [1] Delouis, J. M., Allys, E., Gauvrit, E., & Boulanger, F., Non-Gaussian modelling and statistical denoising of Planck dust polarisation full-sky maps using scattering transforms, 2022, A&A, 668, A122, DOI: 10.1051/0004-6361/202244566
- [2] Morel, R., Rochette, G., Leonarduzzi, R., Bouchaud, J.-P., & Mallat, S. 2023, Scale Dependencies and Self-Similar Models with Wavelet Scattering Spectra, DOI: 10.48550/arXiv.2204.10177
- [3] The project will use the foscat code available on GitHub: https://github.com/jmdelouis/FOSCAT
