Stochastic Expectation Maximization for Robust State-Space Radio Interferometric Imaging

2026-06-24 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Signal Processing & Imaging · Depth: Expert, long

Summary

State-space models provide a flexible framework for analyzing dynamical systems, but conventional Gaussian assumptions often fail to capture heavy-tailed or outlier-prone measurement noise, such as radio-frequency interference (RFI) in radio interferometry. This work proposes a robust estimation scheme for linear state-space models subject to compound-Gaussian noise. The method employs a Stochastic Approximation Expectation–Maximization (SAEM) algorithm, replacing the standard E-step with Monte Carlo sampling of latent states and noise texture via closed-form Gibbs updates, which enables tractable inference despite the heavy-tailed likelihood. Numerical experiments on a synthetic dynamic radio-interferometric imaging scenario, simulating a rotating ring source observed by the Very Large Array (VLA) at 3.8 GHz with 15% RFI contamination, demonstrate that the proposed SAEM method significantly improves reconstruction fidelity and robustness, outperforming a Gaussian EM algorithm and even an oracle RTS smoother.

Key takeaway

For Machine Learning Engineers developing robust imaging systems in noisy environments, you should consider implementing Stochastic Approximation Expectation-Maximization (SAEM) with heavy-tailed state-space models. This approach significantly improves reconstruction fidelity and robustness against non-Gaussian interference like RFI, even outperforming oracle Gaussian smoothers. Your systems will benefit from modeling measurement noise as compound-Gaussian, enabling more accurate joint state and parameter estimation in challenging real-world scenarios.

Key insights

SAEM robustly estimates state-space models with heavy-tailed noise, outperforming Gaussian methods in RFI-affected imaging scenarios.

Principles

• Gaussian assumptions fail with heavy-tailed noise.
• Robustness is crucial in RFI-dominated imaging.
• Compound-Gaussian models restore conditional Gaussianity.

Method

The SAEM algorithm replaces the E-step with Monte Carlo sampling using a block Gibbs sampler. It alternates FFBS for states and Gamma updates for scale variables, handling complex observations via real-augmented representation.

In practice

• Model RFI as compound-Gaussian noise.
• Use SAEM for joint state and parameter estimation.
• Employ FFBS and Gamma updates for latent variables.

Topics

• Stochastic Approximation EM
• Radio Interferometry
• State-Space Models
• Heavy-Tailed Noise
• Gibbs Sampling
• RFI Mitigation

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.