EM Algorithms and Antenna Sub-Array Switching for Interferometric Imaging

Radio interferometers enable observations of the sky at wavelengths invisible to the naked eye, providing valuable information about the universe. With advances in interferometric systems, antenna arrays are now being used as a beneficial replacement for parabolic antennas. The next generation of radio telescopes is based on large arrays, such as the Low Frequency Array (LOFAR) in Europe, which includes around 50,000 antennas, and the future Square Kilometre Array (SKA) in Australia and South Africa, which will comprise 2,000 mid- and high-frequency dishes and aperture arrays, along with one million low-frequency antennas. Thanks to the increasing number of antennas, the sensitivity of new-generation radio instruments is unprecedented. However, data processing and storage pose significant challenges due to the high data rates. Moreover, radio frequency interference (RFI) mitigation has become more critical, given the instruments' heightened sensitivity. To meet theoretical performance limits and fully exploit the potential of such ambitious international projects, signal processing issues must be addressed. Inspired by the flexibility of the SKA, we propose an antenna subarray switching strategy to reduce computational load in radio astronomical imaging. This strategy involves switching between different types of subarrays during observation to benefit from the specific advantages of each. To implement this approach, we begin by designing subarrays. The Cramér-Rao Bound (CRB) is widely used in array signal processing for subarray design due to its asymptotic optimality. However, to overcome CRB's limitations at low Signal-to-Noise Ratio (SNR), we propose using the Barankin-type Bound (BTB) as an alternative criterion. By using subarrays designed based on CRB and BTB, we implement the subarray switching strategy and demonstrate its superiority in terms of the trade-off between image reconstruction quality and computational load reduction, compared to using the full array. To handle RFI within the switching framework, we first model RFI as low-rank noise. This modeling enables the development of a novel subarray switching algorithm based on a variant of the Expectation-Maximization (EM) algorithm. Simulations show that our approach achieves higher accuracy than classical methods that do not account for the presence of RFI. Furthermore, we propose a second model that explicitly takes interference sources into account. This model is based on the class of compound Gaussian distributions. We then introduce a second subarray switching algorithm based on regularized maximum likelihood estimation, of the EM type, in the presence of interferences. However, the switching strategy is pertinent only when the selected imaging algorithm reaches the CRB or BTB, which is not always the case in practice. The performance of switching strategies depends on the imaging algorithm used. To address this, we propose a learning-based probabilistic subarray design method that incorporates the imaging algorithm. This also enables the design of more than two subarray patterns, enhancing the flexibility and potential of the switching strategy. The proposed methods were tested in simulation, and some of them were validated on real data.