Stochastic Expectation Maximization for Robust State-Space Radio Interferometric Imaging

State-space models provide a powerful framework for describing the evolution of hidden states in dynamical systems [3], [4], [1]. Conventionally, state-space models assume Gaussian measurement and state noise, owing to their tractability and well-characterized statistical properties. However, many real-world phenomena are subject to perturbations that deviate from the conventional Gaussian noise assumption. In radio interferometry, for instance, observational data are frequently corrupted by non-Gaussian noise sources such as radio-frequency interference (RFI) [5], [2], which originates from man-made signals and introduces significant distortions into astronomical measurements [6], [30]. Such interference produces sporadic high-power spikes in the measured visibilities, leading to heavy-tailed statistics. Many radio-interferometric reconstruction methods assume Gaussian additive noise [7], [31], [33], [35], an approximation that can lead to inaccurate reconstructions when the heavy-tailed nature of real-world measurement noise is not properly accounted for. In the realm of state-space modeling, addressing non-Gaussian noise has led to the development of various methodological approaches, notably particle filtering and non-conventional Kalman filters. Particle filters [8], or Sequential Monte Carlo methods, are designed to handle non-linear and non-Gaussian state-space models by representing the posterior distribution with a set of weighted samples [9], [10], [32].