Webinar : Rank-one projections for compressive radio interferometric imaging

Rank-one projections for compressive radio interferometric imaging

Radio-interferometry (RI) observes the sky at unprecedented angular resolutions, enabling the study of several far-away galactic objects such as galaxies and black holes. In RI, an array of antennas probes cosmic signals coming from the observed region of the sky. The covariance matrix of the vector gathering all these antenna measurements offers, by leveraging the Van Cittert-Zernike theorem, an incomplete and noisy Fourier sensing of the image of interest. The number of noisy Fourier measurements–or visibilities–scales as O(Q^2 B) for Q antennas and B short-time integration (STI) intervals.

In this talk, we will see how we can address the challenges posed by this vast volume of data, which is anticipated to increase significantly with the advent of large antenna arrays, by proposing a compressive sensing technique applied directly at the level of the antenna measurements.

First, we will understand how beamforming–a common technique of dephasing antenna signals usually used to focus some region of the sky–is equivalent to sensing a rank-one projection (ROP) of the signal covariance matrix.

Then, we will study a compressive sensing scheme relying on random beamforming, trading the dependence of the data size in the squared number of antennas for a smaller number of ROPs. We provide image recovery guarantees for sparse image reconstruction.

Secondly, the data size is made independent of the number B of STI by applying Bernoulli modulations of the ROP vectors obtained for the STI. The resulting sample complexities, theoretically derived in a simpler case without modulations and numerically obtained in phase transition diagrams, are shown to scale O(K) as where K is the image sparsity. This illustrates the potential of the approach.

This is a joint work with O. Leblanc, T. Chu and Y. Wiaux.