Contributions aux méthodes de calibration et d'imagerie pour les radio-interféromètres en présence d'interférences

Radio-interferometers enable the reconstruction of images of radio emissions originating from celestial sources. These images are of great interest to radio astronomers and astrophysicists as they provide information about the underlying physical phenomena in the universe. To achieve this, an initial calibration step is necessary to estimate and correct pertubating effects, particularly those related to the instrument and the propagation of the signal of interest through the atmosphere. Subsequently, imaging algorithms are implemented to reconstruct a sky image. However, the combination of the increasing use of radio frequencies in various human activities and the high sensitivity of the antennas requires the development of robust treatments to address the presence of radio frequency interference (RFI). Several methods exist to detect and filter these interfering signals. Nevertheless, detecting low and moderate power interference sources remains challenging using such methods. The objective of this research is to propose signal processing algorithms for radio astronomy that are resilient to the presence of interfering sources in the data. This work will be conducted with a constant focus on statistical performance and computational efficiency in high-dimensional settings.Firstly, in the context of calibration, we demonstrate that interferences can be modeled as a low-rank noise. This modeling approach has allowed us to develop an innovative multifrequency calibration algorithm based on a variant of the Expectation-Maximization (EM) algorithm. By carefully selecting a latent data space, we obtained analytical expressions at each iteration to limit the required computational burden. The performed simulations have shown the superior precision of the proposed solutions compared to the state-of-the-art methods in the presence of RFI. Subsequently, we propose a statistical data model that accounts for the impact of interfering sources in the imaging context. To do so, we rely on the class of compound Gaussian distributions. Thus, we have been able to propose a regularized maximum likelihood algorithm (EM like) in the presence of interference. However, all the proposed algorithms for solving the maximization step of the EM algorithm involve a Discrete Fourier Transform (DFT), the computational load of which is linked to the expensive implementation of a DFT on a high-dimensional visibility vector. To accelerate this step by employing a Fast Fourier Transform (FFT), we introduced a synthetic noise to account for the approximation of a non-uniform grid DFT by an FFT. This led us to develop an original set of latent variables to improve its computational efficiency. As expected, the proposed imaging algorithms allow for improved reconstruction compared to state-of-the-art algorithms in the presence of RFI, while maintaining controlled computational complexity.