New algorithms for radio astronomy

Optics and lenses are not the only tools for exploring the sky. Radio astronomy studies radio waves, waves with frequencies below 300 gigahertz (GHz), emitted by celestial bodies. These waves are captured by arrays of radio telescopes and analysed using interferometry, a suite of techniques that extracts information from interference patterns obtained digitally. The instruments used construct an image of the sky by combining signals from multiple antennas. In practice, only radio signals in the range of 10 megahertz (MHz) to 30 GHz can pass through the various layers of Earth's atmosphere. These signals are also subject to interference from radio frequencies generated by human activity and nearby celestial objects.

The contributions of radio astronomy

Nevertheless, radio astronomy has been behind several astronomical and cosmological discoveries, including quasars, pulsars and the cosmic microwave background. It is also used to study the Sun, Jupiter and black holes such as the one at the centre of the Milky Way. The arrival of a new generation of radio telescopes, for instance the Low-Frequency Array (LOFAR) in Europe and the Square Kilometer Array (SKA) currently under construction in Australia and South Africa, presents a major challenge in terms of analysing the vast volumes of data produced by systems spanning several countries. Currently, interferometric data are often processed using algorithms based on Fourier transforms - a mathematical tool that converts time functions into frequency functions. However, this approach is proving suboptimal given the exceptional performance achievable with these new instruments.

This is why the team led by Pascal Larzabal, a professor at Université Paris-Saclay and a member of the SATIE laboratory, is developing new algorithmic methods for radio astronomy. "I've been working on antenna signal estimation since my PhD. I'm not an astrophysicist, and the SATIE laboratory is primarily an electrical engineering laboratory, but I began to focus on radio astronomy about ten years ago."

Outdated algorithms

In the early days of radio astronomy, the first radio telescopes were simple parabolic dishes pointed skywards, with the focal point collecting both the signal of interest, but also noise. This noise was averaged and partially attenuated through the measurement of celestial signals. "There are two fundamental parameters here: the surface area of the dish determines sensitivity, while the diameter of the antenna, governs resolution, so as to be able to separate two very close radiating signals. It's a bit like seeing headlights in the distance at night; up to a certain point, you can't tell whether it's a car or a motorbike."

Satellite dishes were made larger in a bid to improve them. Today, the world's largest motorised dish measures 100 meters in diameter, and the record is over 500 meters, although in that case the radio telescope is fixed. "The new generation of telescopes, based on interferometry, consists of arrays of elementary dipoles and parabolic antennas arranged on the ground, ideally in deserts to minimise interference with celestial signals. Computerised delays are applied to synthesise and steer a huge digital parabola with a diameter equivalent to the longest distance between two antenna in the array," explains Pascal Larzabal. From an algorithmic perspective, this involves phase shifting and summing the signals, a technique known as phased array processing. These interferometers are exceptionally flexible, as they can be used to scan the area of interest digitally. They allow for imaging, which is not possible with a mechanically steered dish. However, conventional algorithms, especially those based on Fourier transforms, can no longer keep up."

An optimal statistical method

In light of this, Pascal Larzabal's team proposes using "an approach based on maximum likelihood estimation: a statistical method that is often considered optimal for identifying the parameters of a model capable of making the observed data the most probable." This could enhance all types of observations. 
"In radio astronomy, knowing what you're looking at is essential to observing it properly," says Pascal Larzabal, citing the study of the hydrogen line as an example. Hydrogen accounts for 75% of the Universe's baryonic matter (i.e. protons and neutrons)  and its spectral signature allows scientists to trace it back to the epoch of reionisation. This period began 400 million years after the Big Bang, when matter, previously electrically neutral, began to ionise. It was during this phase when the first stars began to form.

The hyperfine transition of the neutral hydrogen atom appears as a distinctive line in its emission spectrum. This line, centred around 1.420 GHz, experiences a Doppler effect due to the expansion of the Universe, and radio astronomy can distinguish different lines. The intensity of each Doppler line informs scientists about the ionisation level of intergalactic matter at different cosmological times and contains a wealth of astrophysical information. It is a kind of radiograph of the Universe.
 

Breakthroughs on the horizon

Radio astronomy also reveals otherwise invisible phenomena. For example, radio observations of Jupiter reveal "ears" on the gas giant, which are actually magnetic fields not visible to the naked eye. This is known as computational imaging, because data is digitally reconstructed to show features that escape conventional detection methods. Pascal Larzabal's team is currently working with radio astronomers at SKA in South Africa. "We're testing our statistical signal processing and informed learning tools on their real-world signals, always with the aim of improving image quality."

The team is mainly studying simulations, in particular to assess the performance of its methods. Their background in signal processing makes them highly sensitive to the computational load of their algorithms, which are significantly more demanding than those based on Fourier transforms. Moreover, radio telescope calculations are too complex to be carried out at antenna level. They are managed by scientific computing centres and computational imaging working groups, one of which is based at Université Paris-Saclay.

"Even if it's too soon to predict the full astrophysical impact, the techniques we're trying to implement will allow for higher resolution and improved image quality. This could support work on the epoch of reionisation, cosmology, relativity and the transfer of baryonic matter involved in star and galaxy formation."
Several projects are already underway. "As part of the Extreme Computing Lab for Astronomical Telescopes (ECLAT) joint laboratory, we are working with the Astrophysics Laboratory of Bordeaux (LAB - CNRS/Univ. of Bordeaux) on the optimum selection of antennas for imaging the birth of giant star clusters. With the Institute of Space Astrophysics (IAS - Univ. Paris-Saclay/CNRS), we're collaborating on studies of the cosmic web to understand galaxy formation. As signal processors, we want to support astronomers and astrophysicists through the current technological transformations," concludes Pascal Larzabal.

References:

• Nawel Arab, Yassine Mhiri, Isabelle Vin, Mohammed Nabil El Korso, Pascal Larzabal. Unrolled expectation maximization algorithm for radio interferometric imaging in presence of non Gaussian interferences. Signal Processing, Volume 237, 2025.
• Cyril Cano, Mohammed Nabil El Korso, Éric Chaumette, Pascal Larzabal. Kalman filter for dynamic source power and steering vector estimation based on empirical covariances. Signal Processing, Volume 230, 2025.
• J. Wang, M. N. E. Korso, L. Bacharach and P. Larzabal. Low-Rank EM-Based Imaging for Large-Scale Switched Interferometric Arrays. IEEE Signal Processing Letters, vol. 32, pp. 41-45, 2025.
• Yassine Mhiri, Mohammed Nabil El Korso, Arnaud Breloy, Pascal Larzabal. Regularized maximum likelihood estimation for radio interferometric imaging in the presence of radiofrequency interferences. Signal Processing, Volume 220, 2024.