Contact: Adrian Jarret (LCAV)
Synopsis: Reconstruction of radio astronomy images as a sum of components from two dictionaries, using linear inverse problems with a composite penalty.
Level: Master
Sections: IC
Description: One of the main challenges in radio astronomy is to reconstruct an image of the sky from noisy interferometric measurements of the radio waves emitted by some celestial objects. A common approach to tackle this problem is to assume a given parametric form for these objects, usually point sources. With this hypothesis in hand, it is possible to formulate inverse problems that we solve by means of penalized optimization. In this case, the objects to reconstruct are very sparse and thus it seems adapted to use the 1-norm for penalization. We then obtain the commonly used LASSO problem, for which efficient numerical solver exist.
In this project, we would like to go one step further and extend the potential form that the celestial objects can to take, so that we are able to reconstruct not only point sources but also diffuse sources. We then propose a model for sky images as the sum of two components with different properties, one being sparse while the other has some spatial extension. Thanks to recent research works, we know that it is possible to enforce such a model by defining an appropriate penalty term, in the same fashion as what is done with the LASSO. The 1-norm is replaced by a composite Sparse-plus-Smooth penalty. In addition to the challenge of implementing the solvers, this approach introduces two penalty parameters (compared to only one with the LASSO) that have a strong dependence one to each other.
This composite approach has already been tested in different toy examples and seems promising for more complex setups. In this project, we would like to apply it on radio astronomy data generated with a realistic simulation package called RASCIL, provided by the international SKA organization. This framework will generate complex and noisy data, and a lot of care will be required to identify the parameters for good reconstructions. To implement the numerical solver, the student will rely on the optimization package Pycsou for Python, developed and maintained by the EPFL Center for Imaging in close collaboration with members from the LCAV.
Deliverables:
- Python code that implements the reconstruction pipeline, from running the simulations to displaying the solutions
- Quantitative and documented study of the regularization parameters of the model
- Project report that presents the theoretical context and summarizes the experiments and the findings
Prerequisites:
- Basic knowledge in linear algebra and functional analysis
- Experience in numerical computing and object-oriented programming with Python (Numpy, Matplotlib)
- Any experience in (convex) optimization is a plus
Type of Work :
- ~70% implementation: Python code using Pycsou, RASCIL
- ~30% theory: inverse problems, optimization, representer theorems, Dirac recovery
(This repartition might be adapted according to the interest of the student.)
References: