Quantifying uncertainty for unrolled algorithms with application to imaging in astrophysics

Full description

Blind and semi-blind unmixing problems [1] are classical inverse problems in a very wide range of scientific domains from sound processing [2], medical signal processing to remote sensing [3] or astrophysics [9]. In these domains, the fast development of high resolution/high sensitivity multispectral sensors mandates the development of dedicated analysis tools. Figure 1 shows a particularly representative example of a supernovae remnant observed in multiple X-ray bands. For such type of data, the observations can be modelled as the linear or non-linear combination of various elementary physical components, which are to be retrieved by the astrophysicist.
To estimate these elementary physical components, one needs to tackle an unsupervised (when no information is available) or semi-supervised (availability of partial information) unmixing problem. The exact same mathematical problem arises in remote sensing or earth observation for the extraction of elementary components such as water, vegetation, buildings, etc.
Although such problems have already been extensively studied over the last decades, the use of the corresponding algorithms for scientific purposes, such as astrophysics, require interpretable solutions. In particular, it is of uttermost importance to quantify the uncertainties of the estimates of source separation algorithms. So far, very few works have been done in this direction with deep-learning-based algorithms, which depend non-linearly on the input measurement.

To overcome these limitations, the goal of this internship is to investigate uncertainty quantification methods for unmixing algorithms based on dedicated machine (deep) learning tools.
Several research pathways are to be considered. Nowadays, promising ML-based approaches make use of algorithm unrolling models introduced in a general setting by Gregor&LeCun [6]. In a nutshell, the core of this class of inverse problems solvers is a recurrent neural network that mimics the structure of standard iterative solvers (e.g. gradient minimisation methods). Their advantage is that the learning procedure can capture data-dependent information making it more adaptive to the data to be handled. Furthermore, only a limited number of algorithmic parameters are learnt during the training process, making the final solvers having a low computational cost [8]. In the scope of unmixing, we now have investigated with success unrolled unmixing algorithms for sparsity-enforcing algorithms or more recently based on prior built from particular generative models. However, none of these approaches allow for quantifying the uncertainty of the computed solution. To that end, the internship work will explore the development of dedicated stochastic unrolling algorithm architectures. Different research path will be explored, including the design of various architectures, training losses that are adapted to derive uncertainties.
Other research paths might be investigated. The developed methods will be thoroughly evaluated, both on simulated and realistic data sets (e.g. in remote sensing, nuclear physics or astrophysics data sets).
The candidate should be pursuing a Master 2 degree (or equivalent) and have a good knowledge in signal/image processing and machine learning.

[1] Comon P and Jutten C 2010 Handbook of Blind Source Separation : Independent component analysis and applications
[2] Fevotte C, Bertin N and Durrieu J L 2009 Nonnegative matrix factorization with the Itakura-Saito divergence with application to music analysis. Neural computation 21 793–830
[3] Dobigeon N et Al. 2014 Nonlinear unmixing of hyperspectral images : Models and algorithms. IEEE Signal Processing Magazine
[5] Kervazo C et Al. 2020 Use of PALM for l1 sparse matrix factorization : Difficulty and rationalization of a two-step approach. Digital Signal Processing
[6] Gregor K and LeCun Y 2010 Learning fast approximations of sparse coding Proceedings of the 27th International Conference on International Conference on Machine Learning 399–406.
[7] Monga V, Li Y and Eldar Y C 2019 Algorithm Unrolling : Interpretable, Efficient Deep Learning for Signal and Image Processing. arXiv preprint arXiv :1912.10557.
[8] Ablin P, Moreau T, Massias M and Gramfort A 2019 Learning step sizes for unfolded sparse coding. Advances in Neural Information Processing Systems 13100–13110.
[9] Bobin J, Acero F, and Picquenot A 2019 Metric Learning for Semi-Supervised Sparse Source Separation with Spectral Examples. 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
[10] Fahes M, Kervazo C, Bobin J and Tupin F, Unrolling PALM for sparse semi-blind source separation, 10th International Conference on Learning Representations, ICLR 2022.

Location

Saclay

Internship conditions

• Internship duration: 6 months
• Level of study: Bac+5
• Training: Master 2
• Continuation in PhD thesis: Yes
• Application deadline: 1 mars 2024

Useful methods and technics:
Machine learning, deep unrolling

Computer languages and software:
Python, Pytorch

Supervisor

BOBIN JÉRÔME
Phone: +33 1 69 08 75 91
Email :

Head of the laboratory DEDIP / LILAS

Phone: