Maximum de vraisemblance et apprentissage informé pour l'imagerie dynamique en radioastronomie

This thesis addresses the inverse problem of image reconstruction in radio interferometry. Inverse problems aim to estimate the source parameters likely to have generated observed measurements, based on prior knowledge of a forward model. In radio astronomical imaging, solving these problems enables inferring unknown sky images from signals measured by radio telescope arrays. This task is inherently ill-posed and further complicated by incomplete Fourier plane sampling and data corruption from noise, particularly radio frequency interference (RFI). Our contributions focus on developing robust and adaptive statistical inference methods for both static and dynamic imaging. The first part of this work addresses static imaging in the presence of RFI, which appear as outliers violating the standard Gaussian measurement noise assumption. To model these perturbations, we adopt a heavy-tailed Compound Gaussian distribution. The hierarchical structure of this model, which introduces latent variables (textures) modulating the noise variance, naturally lends itself to solution via the Expectation-Maximization (EM) algorithm. To avoid ad hoc assumptions about the texture distribution, we propose an unfolded EM algorithm. This interpretable deep learning architecture, guided by the physical model, learns to estimate textures and hyperparameters directly from training samples. Compared to classical iterative approaches, the proposed method offers accelerated convergence while maintaining RFI robustness and high-quality reconstructions. The second part extends the framework to dynamic imaging of evolving scenes, particularly under short observation times. We first introduce an approach based on the Kalman filter, adapted to a non-standard observation model. However, this methodology exhibits limitations in outlier robustness and relies on known dynamics assumptions. To address these constraints, we develop a unified framework for joint estimation of latent images and unknown parameters in a state-space model. The EM algorithm provides the canonical framework for this joint estimation. The parameter vector includes state and measurement noise covariance matrices, along with parameters for a sparse dynamics model. Specifically, rather than directly estimating the state transition matrix—whose dimensionality is prohibitive for imaging applications—we parameterize it through a geometric deformation field. This modeling approach hypothesizes that inter-image evolution is governed by affine transformations (rotation, scaling) that may vary across iterations. To ensure RFI robustness, the measurement noise is modeled using a multivariate Student's t-distribution. Although robust, this choice renders the E-step of the standard EM algorithm analytically intractable. By exploiting the model's hierarchical structure and conditional Gaussian properties, we derive a partially analytical inference method based on stochastic EM algorithms. These combine Kalman-RTS smoothing, which handles the conditional Gaussian part in closed form, with Monte Carlo sampling to approximate the remaining expectations. The proposed approach enables robust estimation of both image sequences and complete model parameters. Numerical simulations confirm the effectiveness of these methods for reconstructing evolving source images under significant RFI contamination.