Personal web page : http://jstarck.cosmostat.org
Laboratory link : http://www.cosmostat.org
Deep learning (DL) has changed the way of solving inverse problems. Many scientific challenges remain that must be met for its deployment in astronomical imagery: i) taking into account the physical training model, ii) estimating the uncertainties on reconstructed images, iii) generalization, and iv ) the volume of data for scaling up. To quantify the uncertainties, we have introduced a probabilistic DL approach (Remy et al., 2020), which makes it possible to derive the a posteriori distribution of the solution. This requires however to use expensive simulation techniques (MCMC) which does not allow its use in ambitious projects like Euclid or SKA. Several challenges will be addressed in this thesis:
- Develop a new DL method to quantify uncertainties, while enjoying theoretical guarantees of coverage. We will rely on conformal quantile regression, a new method derived from theoretical statistics (Romano et al., 2019).
- Generalization: We recently proposed a new architecture of neural networks (the learnets, Ramsi et al., 2020), which has the advantage of including certain properties of the wavelet transform such as exact reconstruction. This type of architecture should provide a solution to the generalization problem.
- The scaling on data of dimension 3 or 4. It will then be a question of extending the results obtained in order to be able to efficiently handle this type of data.
The last challenge of this thesis will be to set up these new tools to solve problems in two large international projects, for dark matter maps with Euclid and SKA.
 B. Remy, F. Lanusse, Z. Ramzi, J. Liu, N. Jeffrey and J.-L. Starck, "Probabilistic Mapping of Dark Matter by Neural Score Matching", NeurIPS 2019 Machine Learning and the Physical Sciences Workshop.
 Y. Romano E. Patterson E. J. Candès, Conformalized quantile regression. Advances in neural information processing systems 32 NeurIPS, 2019.
 Z. Ramzi, JL Starck, T Moreau, P Ciuciu, "Wavelets in the deep learning era", European Signal Processing Conference, accepted submission to the EUSIPCO 2020 conference.